I have to agree with Capt. Vulcan. By far, Call of Duty 4 Modern Warfare is a good place to start. However, I know the allure of the new hotness can be powerful.
Battlefield has been more of a tactical game with lots of vehicular combat and large maps. This works well when you have a clan of guys to play with. You can select a class of soldier like infantry, engineer, medic and advance each class.
Call of Duty is a bit more faster paced, IMHO and better suited for individual play and can lend itself well to clan play, but nowhere near as cool as BF when it comes to clan play. I know the single player has mediocre reviews, but those are from reviewers who play COD every year. If you've never played COD, there's a good chance you might enjoy the single player. I wouldn't say the same thing about Battlefield. It's single player is usually pretty bad. My favorite mode in COD multiplayer is Kill Confirmed. That's when you shoot a guy, you have to run to his dead body and collect his dog tags to get full credit for the kill. This prevents people from hiding away in 1 spot and killing everyone that passes by.
Both both of these franchises shine in its multiplayer mode. There's room for both in my library, but I'm holding out for the PS4 versions. But if you're a single player fan, I'd recommend Call of Duty 4