Lack basically gave you a good list, but I'll tinker with it...steevee said:snip
Civ V is flat out the best game in the series to date, it has a smoothness and simplicity to it while retaining a lot of the depth of the franchise. Really, if you have any love for Turn Based Strategy this is the one must buy title.
For RTSs, I'd suggest Dawn of War. The Platinum version will run you about $30 US... so unfortunately with Civ V, there goes your budget. If you have to pick a single Dawn of War release, then the one to pick is Dark Crusade. Dawn of War 2 is a completly different game, with less of an RTS base and more action RPG.
For FPSs, the STALKER franchise is excellent, but, and this is a big caveat, it is very unusual. It's much more of a tactical shooter than you're likely to encounter elsewhere, weapons are highly inaccurate and subject to jamming even under ideal circumstances. If you can get past this you'll find a remarkable survival horror franchise.
Borderlands is insanity, pop culture references and blood on the walls, but it is a very solid shooter, and certainly worth mentioning.
Finally Battlefield: Bad Company 2, it's a military FPS in the same vein as the Modern Warfare franchise but with a lot more personality. It's pretty good, but fairly short. I hear good things about the multiplayer as well.
Okay, now, this does vastly exceed your budget, and for that I apologize. You'll have to pick and choose obviously.