SMG: Maliwan. Huge rate of fire means maximum elemental chance
Pistol: Bandit. Huge clip for a pistol is very helpful.
^ Jacobs are my second choice since revolvers do a ton of damage, you can focus on headshots, and they are very ammo efficient. Hyperion pistols are garbage since they start out so innacurate, you're wasting shots trying to get the bullets to fly straight. Maliwan pistols are junk to me since all the bullets have a projectile travel time which is not what you want unless you're desperate for an elemental weapon.
Shotgun: Hyperion. Accurate shotguns YES PLZ. Tediore shotguns are a second choice due to also being somewhat accurate, and the reload is quick. Being in close range with a slow reload is a no-no.
Assault Rifle: Anything works really, except maybe a jacobs rifle with a ridiculously small clip and long reload time (ugh.) I prefer Dahl rifles though since rifles often have a lot of recoil; It's nice to be able to shoot straight.
Sniper: Jacobs, but sometimes Maliwan. Jacobs for obvious reasons, but it's nice to be able to drop elemental effects on enemies from a distance if you want to play it safe against a specific enemy type. Hyperion snipers are junk because you don't need extra accuracy on a sniper rifle. I don't life Vladof since they burn through too much sniper ammo which you don't usually have a lot of.
Rockets: Anything with the highest damage. I like to not waste rocket ammo, so I wont take bandit weapons because they consume 3 rockets at once which is a waste... unless I'm wrong about that. I tend to frown on the Torque launchers with the ridiculously slow nuke-style rockets, though I sometimes take them if the damage is TRULY ridiculous.
Grenades: I'll take whatever has the highest level though I do lean towards damage grenades like MIRVs or sustained AoE. I like the sustained damage AoE grenades like acid cloud, tesla and bouncing betty because the enemies are too stupid to leave the area and you can often melt huge enemies for ridiculous damage because they just sit there.