As someone who started the game from scratch as a gunner, I am no master but I will attempt to give a little advice as I have been decently successful thus far.
Some things to remember at all times:
1. The limited amount of ammo types is a blessing in disguise- it might seem like it's great that the gunner has a page just for ammo, but you're going to fill it- and then some- at all times. You'd never have the (few) slots you have for loot if you could carry all ammo types.
2. The highlighted ammo types on the stats are the kinds of ammo that your gun rapid-fires. THIS IS AWESOME. This kind of ammo should be your mainstay when using that weapon. You get multiple shots, firing very quickly, for the cost of one shot! You'll come to know what kinds of ammo besides this you like to rely on across all missions, and which types are more helpful against certain bosses.
3. Once you have decided on what your main ammo repository for your current gun will be, ALWAYS stock up on them, plus any specific types for the mission at hand, before you head out. Realizing that you have one Para shot too few to paralyze a monster can be the difference between victory and agony!
3. The initial gun selection totally, completely sucks. It starts to open up only after you beat the Urgent Gobul quest. But ultimately, the ability to mix and match and find your ideal gun once everything is available to you makes it the most flexible weapon.
4. Gunners, by nature of their armors, are squishy as fuck. It's unfortunate, but the way it goes. Learn to roll like a spastic hedgehog. Don't try to get that extra shot in before rolling out of the way of an attack unless you've fought that monster multiple times- much better to not take a hit than take slightly less time to beat the boss.
5. The "you can't shoot, your ammo isn't loaded" animation is incredibly punishing. Seriously, it's a joke. It is likely to kill you at least once. Make the Y button your best friend.
6. The status-effect ammos are great, especially online. You can poison, paralyze, put to sleep, exhaust/stun, and generally fuck with your target reliably at least once each per fight, and in a matter of a few seconds if you land your shots. The key is tailoring when to use each to each fight. Poison is usually a good way to start a match and take a monster's hp down a bit. Paralyze makes a great setup for switching to crag/clust and getting a few huge shots off with impunity. Putting a monster to sleep, laying a trap right under it, kicking it in the face, and tranqing is one of the most satisfying ways to capture.
7. Keep your distance. I have trouble with this one myself as I love shotgun-style gunning. But seriously, due to the aforementioned squishiness, it's always a good idea to put some space between yourself and your foe, even if you're kicking ass.
8. Be patient! I haven't tried all the weapons, but gunning can be an incredibly frustrating experience if you rush or try to do too much at once... but also incredibly rewarding when it pays off.
Hope to see you guys online!
EDIT: Some definitions:
Deviation: How much your shots move to the left or right. Certain gun parts will show L/R or Low L/R or so on, or just Low R, to indicate how the shots will be affected. Other parts that say things like reduced or increased will make this better or worse.
Recoil: The amount of time it takes before you can take another shot. Obviously this varies a lot between ammo types, but this is a global modifier.
Reload: Obviously, the time it takes you to load new ammo- this is the same for all ammo types.
Sheild: Some guns let you block! I've never tried one, but it must be really useful if you've got it.