Get a corrosive SMG as soon as you can and upgrade to a better one whenever possible, you'll need it for fighting Robots. Get something with Shock and keep upgrading, this will help when you get to the Stalkers. It's best to have at least one of each (Pistol, SMG, Assault Rifle, Shotgun, Sniper, Rocket Launcher) just so you can swap if you run out of ammo of another type. Other than that, experiment and use what works for you.
Grabbed this today, on a bit of a whim. Friend of mine just played through the first game and got this almost straight away, so I thought I'd join him.
Didn't really feel compelled by any of the character choices... Ended up going Commando, so to speak. Unfortunately that was my mate's choice, too. Bit overwhelmed by all the guns, but I did anticipate that, to a degree.
Suppose I'll need to try out each class a bit.