Borderlands Co-Op Lan Play - Guns and Ammo
Loot is "first come first served": only one copy of each item exists for all players to share. This goes for both ammo, guns, shields, grenade mods, ... Everything. The only thing that is awarded "privately" for each player is quest rewards.
Not specializing in the same gun types could be beneficial, but I don't honestly think you'd have too much issues if you used the same kind of guns.
And yes - you can play the same class, if you so desire.