The main advantadge on any Martial character after level 5 is iterative attacks. Using a barbarian with these starts will definitely let you get an early start with reduced power as you level higher.
Shifter's Blessing doesn't kick in until Ranger level 3, which will give you 2 levels of Barbarian at level 5.
This means you'll have a total of 4 Feats + 1 rage power. I would suggest taking Power Attack at level 1, Rending Claws at 2nd, Extra Rage Power at 3rd (Assuming you have a level of Barbarian by now), and Amplified Rage at 5th.
Improved Natural Attack:Gore is worth looking into as your level 7 feat as well.
This will make sure that you do have Rend with your claws, and that while shifted and Raging, you will have a +13 to hit with all attacks, or +11 while Power Attacking.
This however won't let you gain extra attacks as your BAB increases at later levels, and there are a couple of issues.
Abyssal Blood is a level 6 power, and as such can only be taken by a character with 6 class levels in Barbarian.
The middle blood rage power (that without "lesser" or "greater" in the title) can only be taken by a 6th level or higher barbarian that already has the lesser blood rage power of its group.
If you were to compare your single attack damage against a fighter of a similar level, I think you would fall short of damage in a case by case basis, though as your build focuses on Full Attacks, this is an acceptable turnover.
On any given attack vs a monster with 17AC, you've got about a 25% chance of missing. Assuming you hit every attack, you'll be dealing around 70-80 damage with a full attack, and at most with one attack, you'll hit 26 with your Gore.
This AnyDice Link will show the average damage you can expect for each attack.
Two-handed weapons are not useless: bonus action and TWF
The two weapon fighting that a barbarian can use is not the same as the Fighter/Ranger fighting style option "Two-Weapon Fighting." Only that class feature allows the Fighter/Ranger to add their Ability Score Modifier to the second weapon's damage.
Each successful attack (using Strength) gets the Rage damage bonus
Assume a barbarian of Level 1-8 (+2 rage damage) with a Strength of 16 (+3 damage modifier).
The Two-Weapon Fighting rule (Chapter 9) states:
When you take the Attack action and attack with a light melee weapon
that you’re holding in one hand, you can use a bonus action to attack
with a different light melee weapon that you’re holding in the other
hand. You don’t add your ability modifier to the damage of the bonus
attack, unless that modifier is negative.
The Barbarian has to use a bonus action to trigger their Rage (PHB, Chapter 3):
In battle, you fight with primal ferocity. On your turn, you can enter
a rage as a bonus action. {snip}
When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table.
Let's see how a three round battle will go.
- Round 1. Trigger rage plus one 2H weapon attack, or trigger rage plus one hand axe attack.
- Round 2. One attack with 2H weapon, or two attacks with two weapons w/ STR bonus damage on only one.
- Round 3. One attack with 2H weapon, or two attacks with two weapons w/ STR bonus damage on only one.
Damage comparison
Two-handed sword versus two hand axes: damage if we presume that all attacks hit
Round 1: 2d6 + Rage + STR modifier (2d6+5) vs 1d6 + Rage + STR modifier (1d6+5)
Advantage 2H weapon.
Round 2: 2d6 + Rage + STR (2d6+5) vs [1d6 + Rage + STR] + [1d6 + Rage] (2d6+7)
Total after two rounds is: 4d6+10 (24) vs 3d6+12 (22.5). Slight lead to 2H weapon.
Round 3: Same as Round 2, but now TWF takes a slight lead, since:
All told, we see 6d6 + 15 from the 2H weapon. (Average 36)
All told, we see 5d6 + 19 from the TWF choice. (Average 36.5)
Note: you gotta hit it to damage it.
An advantage accrues to the TWF approach if the fight lasts that long due to having more chances to hit. There are two chances to hit on the second and third rounds, whereas with the 2H weapon, there is only one chance to hit on each turn. You'll have a total of 5 attack rolls, rather than 3 attack rolls, if the dwarf goes with the two hand axes.
With that in mind, DerekStucki did an analysis of the choices confronting the Barbarian and suggested carrying both a Two Handed Weapon and two light one handed weapons. Why? Because the conditions of combat vary.
For what it's worth...
If the Barbarian takes the Dual Wielder Feat at level 4, they can use 1d8 damage dealing warhammers, battle axes, or long swords. The longer the battle goes on, the more two weapon fighting approach looks to be more advantageous. But, after level 5 where the Barbarian gets two attacks, this changes things enough that you may see the 2H weapon being a good or better choice.
- We have a number of Q&As that compare TWF with 2H-weapons that go
into far more detail about that. Since you are dealing with a
beginner that's not germane for this question. If she gets to level 4 and considers that feat, I suggest you drop a question here to ask about the pros and cons of the Dual Wielder Feat for a Barbarian versus fighting with two-handed weapons (and the related analysis of whether Great Weapon Fighting would be a a feat worth taking).
The same three round fight with the dual wielder feat, at level 4, using battle axes (1d8) as one handed weapons, yields this result after three rounds
All told, we see 6d6 + 15 from the 2H weapon. (Average 36)
All told, we see 5d8 + 19 from the TWF choice. (Average 41.5)
Round 1 is still "advantage 2H weapon" and Round 2 is roughly a tie.
This looks to be a little more attractive, except during the first round, and the 5 versus 3 attack rolls means that there will be fewer misses. Each miss by the 2H weapon is a bigger loss of damage to the target.
Things change at 5th level for most martial characters
The 2H weapon barbarian gets another spike in attractiveness at level 5, so early rounds tend to favor the two handed weapon.
The Two-Handed Weapon Barbarian gets two attacks. TWF gets three on rounds 2 and subsequent, using the bonus action. Damage summary:
Round 1: 4d6 + 2STR + 2Rage for 2H vs 2d8 + 2STR + 2Rage for TWF
Round 2: 4d6 + 2STR + 2Rage for 2H vs 3d8 + 2STR + 3Rage for TWF
(All subsequent rounds are per Round 2.)
The fight has to go on for a bit longer than two rounds for the TWF to begin to show advantages.
If the Dwarf does not take a feat, but instead boosts Strength to 18 at level 4, all attacks hit more often, all attacks get another damage point boost from strength, and the 2H weapon approach begins to look more attractive.
Best Answer
Yes, you can make 1 greataxe attack and 2 claw attacks
There are 2 parts to this question:
Fortunately, the answer to both of these is yes.
Having claws doesn't prevent wielding weapons
The main concern here is the first clause of the Form of the Beast's "Claws" option: "Your hands transform into claws," and whether this implicitly prevents you from doing anything that would normally require hands, such as wielding weapons or manipulating objects. However, there are a number of clawed creatures that can also wield weapons, such as a mezzoloth:
As well as the dragonborn player race, which has no racial limitations on weapon use despite having clawed hands:
Hence, there is no implicit mutual exclusion between clawed hands and weapon use. So, given that the Form of the Beast feature doesn't specify that your hands become unusable as normal hands while transformed, there is nothing preventing you from wielding weapons while your hands are transformed into claws.
You can attack with a two-handed weapon and then your claws
You might also think that a two-handed weapon would render your claws unusable, unless you attack with the weapon and then drop it. However, post-erratum, the two-handed weapon property says (emphasis added):
This means you can attack once with your greataxe in both hands and then let go with one hand in order to make a claw attack, without dropping the weapon. This satisfies the requirements of the Form of the Beast feature in order to gain the additional attack: you have taken the Attack action on your turn and made an attack with your claws. Hence, you can make one attack with a weapon (even a two-handed one) and then 2 attacks with your claws in a single attack action.
You can even use two-weapon fighting and your claws together
With some creative object interaction, you can even make 4 attacks per turn: 2 attacks from your claws and 2 weapon attacks using two-weapon fighting. For instance, you can begin your turn wielding 2 shortswords. You take the attack action and make one attack with a sword, then use your bonus action to attack with the other sword. Then, you put away one sword and use the 2nd attack of your action to attack with your claws, allowing you to make one more attack with your claws, for a total of 2 shortsword attacks and 2 claw attacks. On your next turn, you start with 1 shortsword in hand and one free hand. You make your two claw attacks first, then you pull out your 2nd shortsword and make your 2 shortsword attacks using two-weapon fighting.
Note that, per the two-weapon fighting rules, you don't add your ability modifier to the 2nd shortsword attack, so I don't think this will improve your raw damage output over a greataxe. However, this might be useful for situations such as fighting a mage, where more attacks means more chances to break the mage's concentration.