To go by the inventory at Friendly Fire, SR3 sports a surprising lack of weapon diversity (two weapons at the same price in each of Pistols, SMGs, Shotguns, and Rifles), which suggests that the differences between them are fairly marked (i.e. that it comes down to more than personal preference).
However, those differences aren't well explained within the game (for example, the phrase "higher grade" is used several times, with no explanation as to what that means) and I know that some weapons aren't available until found or unlocked, which makes comparison even more difficult.
What (permanent) weapons are available and how do I get them? What are the basic differences between the weapons in each category that one would use to choose between them?
Best Answer
There's a full weapon list here, and most weapons support upgrades, which you can find a list of here. I'd suggest focusing on one weapon early on and getting it to level 4. By the end of the game, you will have enough cash to own each weapon in each category. At one point you'll also be given the choice to take a weapon upgrade cost discount, so if the upgrades seem overpriced, keep playing the story missions.
Also note that in the upgrade menu on your phone are various upgrades for enhancing your bullet carry capacity and reload speed, and these are quite useful.
You can save a good amount of money by picking up enemy weapons. Even if you love the one you've got, picking up and dropping one an enemy left behind will unlock that weapon in your crib and Friendly Fire for further use/upgrades.
Some personal observations/strategy:
Melee
Pistols
SMGs
Shotguns
Rifles
Explosives
Grenades
Special
There's a wide variety here, and you'll unlock them slowly as you play story missions. Personally I preferred the RC Possessor, simply because at level 4 it can take out any military vehicle with one shot (and explode it to take out other targets). Plus it's one of the easiest ways to get some of the flying military vehicles in the game. If you shoot a VTOL/chopper with it, and land the craft, the pilot will generally jump out and leave the keys in the ignition.
The sniper rifle is a required weapon at times (Guardian Angel missions, primarily) and it's pretty good as snipers go, no sway and 3 zoom levels. It's not really a snap-shot weapon though, and it isn't as useful in as many situations as the Annihilator is. You're more likely to have at least a half dozen guys on you, or a fast-moving brute than you are likely to see one guy at range that the pistols can't handle.
Some of the other special weapons will be most useful in the areas where they're given to you (the airstrike and missile drones come to mind, for instance). They're fun to play with, but from a practical perspective aren't that useful.
When you start to get up close to level 50, infinite ammo upgrades will be available for all weapons. Grenades are excellent for this, especially combined with explosive resistance. Second on the list is Annihilator ammo. Once you have explosion immunity and infinite explosives, you are an unstoppable killing machine.
Once I had those upgrades, I went for infinite pistol ammo, because it's a high damage, high accuracy weapon that's got a wide variety of uses. Compared to the explosive damage of the Annihilator though, it's a distant second or third.
There's also an achievement for having a level 4 upgrade to one weapon in each class. Note that I believe this includes grenades, and you have to upgrade the baseball bat (the only melee weapon that supports upgrades) in order to get this.