I have two recommendations:
1. BioShock (XB360, PC) - It has a compelling and interesting story, upgradeable weapons, three types of ammo per weapon, and psychic powers. The combat is fun and creative, as you can shoot enemies, set them on fire, freeze them, zap them, or set them to fighting each other!
2. The Orange Box (PS3, XB360) - It's basically five games in one, although one is an online-only game. It has Half-Life 2, HL2 Episode 1+2, Portal, and Team Fortress 2. The Half-Life games are quite well-done in terms of gameplay and story. Portal isn't really a shooter, though. It's more of a first-person puzzle game but it's challenging and addicting.
As individual tastes may vary, it'd be a good idea to rent before purchasing. Also, these games have been out for a while, so you should be able to pick them up used. I got BioShock from Rogers and The Orange Box from Electronics Boutique.