if you wanted a purely generic FPS you can go Killzone like the trolls here say. But COD is probably the best place to start. Battlefield has a lot more to learn then the COD franchise when it comes to gameplay and mechanics. Plus i think the smaller maps will make it easier to get the hang of it.
Huh? It has a pretty big focus on gun play. It is definitely teamwork but not as vehicle-dependent as you think. Campers also get blown up pretty easily.
Maybe it's just me but vehicles respawn far too quickly. Many people don't even use their guns, they just wait till they respawn so they can use them again. Also, if there's a guy that's a pro with a jet, no one will take him out. He'll wipe out the airspace while killing anyone near objectives simultaneously. Others just spam grenades at objectives while replenishing them.
Sure there's always noobs running around that you can kill, but it's far better being good with vehicles than being good with guns
Battlefield 4 because it does more than any of those other shooters. 64 player multiplayer, vehicles, destruction, dynamic weather... The list goes on. It does all that and manages to have better visuals than Call of Poopy and MW2: Mechs Edition.