Modern Warfare 2 will be the biggest when it launches in 3 days. Its single player campaign is very cinematic and the online multiplayer will be extremely popular. These games go for realism, so you’ll see real-world weapons and scenarios.
Left4Dead and Left4Dead 2 have great multiplayer and you play cooperatively with other people online, rather than against each other. This is a zombie apocalypse survival game, so not very realistic from a scenario point of view, but the graphics and animation are great.
Team Fortress 2 is really popular and has a ton of mods available and is constantly being added onto by Valve. It’s class-based so you can play a medic or sniper or scout. This goes for a cartoony but unique atmosphere with a great sense of humor and focus on having fun.
Half-Life 2 and the episodes are still my personal favorite, though it is only single player (but Team Fortress 2 comes with Half-Life 2 if you buy the orange box). Half-Life 2 is set in the future so it isn’t really realistic as in working with real-world weapons and things, but the story and characters are great and it’s one of the most polished games you’ll ever play.
Fallout 3 isn’t really an FPS, more of a role-playing game that happens to be first person. You can pause the firefights and target specific parts of your enemy’s body and your chance for success is based on your skills in certain stats. Great environment and exploration though. Single player only.
Borderlands is similar to Fallout 3 but there is no pausing, just upgrading your weapons and skills like an RPG, and gaining custom abilities with skill points. It can be played cooperatively with 3 other people online or by yourself.
Bioshock is a great single-player FPS with a really unique and thorough atmosphere and story. Your character gets magic abilities to use as well as guns.
Pretty much all of these games are available on both the 360 and PS3, as well as Windows. There are other big FPS games out there, but those are the ones I thought of off the top of my head and that I have experience with.
I would personally buy Modern Warfare 2 at this point. Its online will be popular and give you a lot of replay value with all the unlocks and everything.
If you want the most game for your money, buy the Orange Box which has Half-Life 2, both episodes, Team Fortress 2, and Portal which is one of the most unique and hilarious games ever made. The Orange Box would keep you occupied for hours and hours on each of the games.