For reference, the text of these feats:
Dirty Fighting
You can take advantage of a distracted foe.
Benefit(s): When you attempt a combat maneuver check against a foe you are flanking, you can forgo the +2 bonus on your attack roll for flanking to instead have the combat maneuver not provoke an attack of opportunity. If you have a feat or ability that allows you to attempt the combat maneuver without provoking an attack of opportunity, you can instead increase the bonus on your attack roll for flanking to +4 for the combat maneuver check.
Special: This feat counts as having Dex 13, Int 13, Combat Expertise, and Improved Unarmed Strike for the purposes of meeting the prerequisites of the various improved combat maneuver feats, as well as feats that require those improved combat maneuver feats as prerequisites.
vs.
Improved Unarmed Strike
You are skilled at fighting while unarmed.
Benefit: You are considered to be armed even when unarmed—you do not
provoke attacks of opportunity when you attack foes while unarmed.
Your unarmed strikes can deal lethal or nonlethal damage, at your
choice.
Normal: Without this feat, you are considered unarmed when attacking
with an unarmed strike, and you can deal only nonlethal damage with
such an attack.
There's an obvious comparison of the listed primary benefit of each feat which is fairly trivial; unless you are specifically intending to fight unarmed, Dirty Fighting is a more generally useful feat. Flanking occurs far more frequently than an armed character being separated from their weapons and forced to fight unarmed, but Improved Unarmed Strike is mandatory for any unarmed combat specialist.
However, as wild-shaping Druid, you are not playing an unarmed combat specialist - your attacks are natural weapons, not unarmed strikes, so you already count as armed and do lethal damage - so Improved Unarmed Strike by itself is no use to you. You are only interested in Improved Grapple. Dirty Fighting's special quality enables you to qualify for Improved Grapple without needing Improved Unarmed Strike. It also allows you to take many other Improved Combat Manoeuvre-type feats without having to meet certain other prerequisites. This seems intended specifically as a way to make those combat feats available to a wider range of characters without needing to pay an onerous feat tax (Combat Expertise particularly is much loathed in this regard) or meet Int/Dex requirements. Dirty Fighting may be the only way for low Int/Dex characters to qualify for many combat feats.
However, Dirty Fighting also only counts as Improved Unarmed Strike for the purposes of Improved Combat Manoeuvre feats and feats that have Improved Combat Manoeuvre feats as pre-reqs. Specifically, there are many feats that have Improved Unarmed Strike as a prerequisite that are not Improved versions of a combat manoeuvre, and thus Dirty Fighting does not help you to qualify for taking those. Most of those feats are only useful when using unarmed strikes so they would not be helpful while you are wildshaped, but a few could be applicable to your natural weapons. If you planned to take those feats, you would still need to take Improved Unarmed Strike.
Ultimately, Dirty Fighting is a generally superior feat for those who do not actually want to fight unarmed. You should retrain Improved Unarmed Strike to Dirty Fighting as it will provide you a much greater benefit.
Allosaurus > Giant Squid > Behemoth Hippo >Corpse Lotus
As long as the creature has grab and constrict, you gain those qualities and no other special ability that increases grapple damage. All wild shape-related spells (beast shape, elemental body, plant shape, etc) state that you only gain the listed qualities.
So as long as you assume a form with those qualities, you gain them, and your damage is based on your own stats (and feats) and your size while on that form. So there won't be a best form, but forms that are better on given situations.
Also, the number of attacks matters little if your objective is to cause damage while grappling, as you won't gain the ability to grapple multiple creatures at once, but i listed them for a few creatures that have a considerable amount of natural attacks per round. Also note that some attacks are different from the Natural Attacks table from the bestiary, as some GM's enforce that table instead of what is listed on each creature's entry (which accounts for feats and special qualities), but for this answer we will assume that this is a case of specific ruling overriding a general rule and keep the creature's damage dice.
I will mention when an attack is secondary, so it deals 50% str damage, or when a creature has a single primary attack, so it deals 150% str damage. Otherwise we can assume they are primary attacks that deal 100% str damage as normal.
Lastly, i know you said "no water creatures", but i will list them for completeness of the answer, you can ignore those.
Best animal form
Works as Beast Shape III, which can grant the following abilities if the creature has any of them:
- Huge size, burrow 30 feet, climb 90 feet, fly 90 feet (good maneuverability), swim 90 feet, blindsense 30 feet, darkvision 60 feet, low-light vision, scent, constrict, ferocity, grab, jet, poison, pounce, rake, trample, trip, and web.
The Giant Squid (huge animal) form would grant these abilities:
Low-light vision, swim 60 feet, jet, grab and constrict. Has 5 natural attacks. But the GM might rule that you cannot move on land. Has a single bite attack (2d6), 2 arm attacks without grab (1d6), and a single "tentacles" attack with grab (secondary, 4d6 damage).
Huge animal: +6 size bonus to your Strength, a -4 penalty to your Dexterity, and a +6 natural armor bonus.
The Giant Octopus (large animal) will grant:
Low-light vision, swim 30 feet, jet, poison (1d3 str), grab and constrict. Has 9 natural attacks, one being a bite (1d8 with poison) and the others tentacles with grab (secondary, 1d4), and has a land speed.
Large animal: +4 size bonus to your Strength, a -2 penalty to your Dexterity, and a +4 natural armor bonus.
The Allosaurus (huge animal) will grant:
Low-light vision, scent, grab, pounce, rake. Has a bite (2d6 plus grab) and two claws (1d8 each).
Huge animal: +6 size bonus to your Strength, a -4 penalty to your Dexterity, and a +6 natural armor bonus.
A special note here about Rake, this special ability will grant you a bonus attack against grappled foes, which works similarly to constrict, but do not automatically hit. In this case, might even do higher damage, since the creature can basically make a full-attack while grappling with a single grapple check.
The Megalania (huge animal) will grant:
Low-light vision, scent, swim 30 feet, grab, poison (1d4 dex). Has a land speed, but no constrict ability, which might be compensated by the poison, which will reduce the target's CMD every time they take poison damage. Has a bite attack (single, 2d6 plus poison).
Huge animal: +6 size bonus to your Strength, a -4 penalty to your Dexterity, and a +6 natural armor bonus.
The Hippopotamus, Behemoth (huge animal) will grant:
Low-light vision, grab, trample. No constrict, but has the strongest bite (single, 4d8) damage of land animals, if you include Improved Natural Attack (Bite), we are looking at a strong candidate.
Huge animal: +6 size bonus to your Strength, a -4 penalty to your Dexterity, and a +6 natural armor bonus.
Best elemental form
Works as Elemental Body IV, which grants:
- Huge sized, immunity to bleed damage, critical hits, and sneak attacks while in elemental form, damage reduction 5/—, and elemental abilities based on size, such as burn, vortex, and whirlwind.
The problem here is that none of the elemental forms available have grab or constrict. So, though they are useful forms, none will take great advantage of your build. The "best form" here is whichever grants you the highest strenght bonus, the Earth Elemental (+8 strenght).
However, there are other possibilities here. The Air Elemental will allow you to grapple and fly with your foe, and if they happen to release the grapple, they will take fall damage. The Fire Elemental will allow your grapple to cause extra fire damage with the Burn ability. The Earth Elemental will allow you to grag your enemies underground, where you can probably release them and wait for them to suffocate if they cannot dig their way out.
The extra damage from Burn is complicated to calculate due to it's non-stackable nature and variable duration, but you can assume that the damage should add a constant 2-12 extra damage.
Best plant form
Works as Plant Shape III, which grants:
- Huge sized plant, damage reduction, regeneration, trample, energy resistance 20, vulnerability (which we want to avoid), darkvision, low-light vision, constrict, grab, and poison.
The Corpse Lotus (huge plant) will grant:
Darkvision, low-light vision, DR 10/slashing, energy resistance acid/eletricity 20, grab and constrict. Has 4 vine attacks (1d8 plus grab each).
Huge plant: +8 size bonus to your Strength, a -2 penalty to your Dexterity, a +4 size bonus to your Constitution, and a +6 natural armor bonus.
The Assassin Vine (large plant) will grant:
Low-light vision, energy resistance fire/cold/eletricity 20, grab, constrict. Has a slam attack (single, 1d8).
Large plant: +4 size bonus to your Strength, a +2 size bonus to your Constitution, and a +4 natural armor bonus.
The Sargassum Fiend (large, aquatic plant) will grant:
Energy resistance cold 20, DR 5/slashing, grab and constrict. This is the plant creature with the highest constrict damaged listed on official books (2d8). Being an aquatic (seaweed) plant, it might not be available to your character, but it is worth listing here.
Large plant: +4 size bonus to your Strength, a +2 size bonus to your Constitution, and a +4 natural armor bonus.
The Fungus Queen (medium plant) will grant:
Darkvision, low-light vision, DR 10/cold iron or good, resistance to eletricity/acid/cold 20, grab and constrict. Has 2 claws (1d6) and 4 tentacle attacks (secondary, 1d4 plus grab), though their damage is low for being a medium creature.
Medium plant: +2 size bonus to your Strength, a +2 enhancement bonus to your Constitution, and a +2 natural armor bonus.
The Tendriculus (huge plant) will grant:
Low-light vision, regeneration 5 (bludgeoning or fire), energy resistance acid 20, and grab. No constrict, but you gain regeneration, so i listed it here for it's general usefulness. Has a bite (2d6) and 2 tentacle attacks (secondary, 1d6), all with grab.
Huge plant: +8 size bonus to your Strength, a -2 penalty to your Dexterity, a +4 size bonus to your Constitution, and a +6 natural armor bonus.
Spreadsheets
Community members at paizo.com created spreadsheets that can help druids to pick the best form for certain levels and specific situations. You can easily download them and create column filters to narrow down your search.
That said, the most DPR is probably from the Allosaurus, with 2d6+str and 1d8+str x2 per grapple check, which can use all three attacks on the very first round using the pounce ability. If this is a 18 str druid, we are looking at a +7 str bonus per attack (str 24), or 6d6+21 plus 6d8+42 (bite 2d6+7 and two claws of 1d8+7 each) if all attacks hit. Minimum 75, maximum 147, average 111 damage. On the second round and forward, you can also use his rake ability to keep causing this damage every round after the first.
If the assumed form is that of a Corpse Lotus, we are looking at 6d8+48 per round (str 26). The constrict will automatically hit, but the damage output is still much lower. However, you gain a few extra defensive abilities. Minimum 54, maximum 96, average 75 damage.
Note that even with 2d6 Burn ability and being a Huge creature, the Fire Elemental grants no size bonus to your strenght, so you are using only your character strenght to cause damage here. Best case scenario, we are looking at 2d6+4 plus 2d6 fire damage per grapple check, or 12d6+12 if the target has absolutely no fire resistance (nearly a third of the creatures do). If they have energy resistance (fire) 10, then the fire elemental is no longer a viable option. Including the catch on fire damage (2-12), we have a minimum 26, maximum 96, average 61 damage.
The Behemoth Hippopotamus has the strongest natural attack and is one of the best candidates, even without constrict. With 4d8 bite damage and 24 str (+7 * 1.5: +10 for being a single primary attack), we are looking at 12d8+30 damage per round. Minimum 42, maximum 126, average 84 damage, higher average damage than the Corpse Lotus.
If aquatic creatures are allowed, the Giant Squid is also pretty strong, with it's (secondary) "tentacles" attacks doing 4d6 damage plus constrict, his bite with 2d6+7 and two arms with 1d6+7, the scenario would be 24d6+18 per round (str 24, +3 damage for being a secondary weapon), or 4d6+3 (tentacles) plus 4d6+3 (constrict). Minimum 42, maximum 162, average 102 damage.
You could also consider other tactics might result in more damage, such as mantaining the grapple as a free action and making a full attack. For example, the Giant Octopus makes a total of 9 attacks (bite and 8 tentacles), plus a constrict. With 24 str, that is a +7 bonus on the bite attack and +3 on the tentacles (secondary), for a total of 16d4+48 plus 1d8+7 (with poison) from his bite. Assuming all attacks land, that is minimum of 72, maximum of 127, average of 99 damage.
Best Answer
Most effective is subjective, but it's fairly easy to make excellent use of your grapple feats and wild shape.
To really pull this off, you need to select a form with grab and constrict, such as a hangman tree, a huge anaconda (14 HD Huge variant of the listed constrictor snake, per the last sentence in the description), or in aquatic environments, the giant squid. If you want to include the Vermin Shape spell in your arsenal, you get access to the very excellent Giant Scorpion, albeit only for a few minutes.
Constrict lets you effectively double the damage you deal on each grapple check, which will outpace added attacks from rake or other similar abilities. Grab is vital because it lets you attack normally and make a free grapple check if you hit. This is most important on the first round because you've got a one-round setup time for your tricks.
The per-round flow looks like this:
Round 1
Since you started in your wild shape form, either close with the opponent and attack once or start in range and full attack. Because your attack has the grab special ability, make a free grapple check. If the check fails, repeat this next round until it's successful. If it succeeds, deal constrict damage in addition to the damage that attack deals.
NB: Because you're just starting the grapple, Greater Grapple (and consequently Rapid Grappler) doesn't apply.
We'll assume your opponent doesn't escape on their turn. If they do, start over.
Round 2
Because of Greater Grapple, make a grapple check as a move action to maintain the grapple. If successful, deal damage with your highest-damage natural attack plus your constrict damage. Then, make a grapple check as a standard action, either to maintain the grapple or just inflict damage.
If either of these checks succeed, your Rapid Grappler feat triggers and you can make a third grapple check to deal damage.
In huge anaconda form, you can deal up to 12d6 plus 9 times your Strength bonus per round (3 grapple checks per round, dealing 2d6 + 1 1/2 Strength for the bite and an equal amount for constrict). Giant squid form roughly doubles this damage.
Round 3+
Basically the same as Round 2 until your opponent escapes or dies.
You can choose the natural attack which deals damage explicitly in the Grapple rules:
This does mean that if your form has a natural attack which inflicts poison, you can use that attack on successful grapple checks and still inflict constrict damage.
I caution against pinning an opponent in lieu of dealing damage because it will cause you to lose your Dex bonus to AC, which opens you up to a whole world of pain from your opponents. The increased damage you'll take is unlikely to be a good trade off for keeping your victim from doing much of anything.