Max Payne should be dirt cheap by now and while it's a dated shooter it has a good story told cleverly throguh a graphic novel approach and the atomspher is dark and gritty and feels like somthing out of sin city
Sillent hill 2 and 3 are great if your into the survial horror genere, they too have wonderful stories (sillent hill 2 especially) and are actually quite creepy
Resident Evil 4 is one of the best games i've ever played (and continue to play regularly)
it has action tension, some decent funny moments and it never seems to fucking end so you'll get a lot of bang for your buck.
Grand theft auto Vice City, this should be a no brainer
Mercenaries is big explosive fun. It's like grand theft auto but with air strikes and well structuered missions.
Def Jam Fight for New York is the only head to head fighter i've ever played that actually had a good story mode. you get to creat a character and cutomize his fighting style to your likeing and then go to town on a bunch of rappers. It doesn't matter if you like rap or not, the ability to team up with Ice-T and beat the shit out of Omar Epps is fantastic!
Odin Sphere is a very very pretty side scrolling action RPG. It's featuers gourgeous sprite based artwork and is almost completly voice acted. it has a world of novel ideas and mulitpule stories that you switch between.
Burnout Revenge is a sweet racing game that fast, pretty, and lets you choose from a varity of fun racing modes as well as doing crash courses where the object is to rack up as much points in a single crash on a pre set course.
The Prince of Persia Trilogy should be another no brainer
I'm not a big sports fan so i can't help you there
so that should be enough to get you started