The Marine campaign is really the only one to play cooperatively. Only aliens, praetorians, and predaliens will spawn so there's no point in running through levels that don't have them (including all the alien's levels and the first two predator levels). Since the spawns are the same as in single-player, cooperative play cuts down on the difficulty. But considering it's an already relatively challenging campaign, coop mode for two players works well, especially for casual players. There are some issues, though. For instance, a predator that must be beaten to trigger an event in Tyrargo will not spawn, and neither will the alien queen spawn in cooperative mode so you won't get an epic boss battle at the end.
There are edited maps (dubbed the B-maps for their name, such as Derelict_B, etc.) that have a much higher number of aliens, probably designed for more than two players. One should expect to die a lot on those, not as much on the regular maps.
Keep in mind the order of missions for the marine campaign is: Derelict, Colony, Invasion, Orbital, Tyrargo, and finally Hangar in case you wish to run through them in order.