Right, with all things, I would suggest you start at the beginning. The first ORIGINAL game for the PS is known more for its blend of horror (for its time) as well as its camp values. If you want something more straight horror and devoid of Jill sandwiches, play the remake for the GCN, which they have also ported onto the Wii.
The 2nd game introduces you to Leon Kennedy, which has become more or less the "hero" of the RE series after RE4 and after Chris Redfield from RE1 begun dabbling with cow steroids (more on this later), as well as Chris' sister Claire. This is actually considered to many to be the hub game, as it show more about the "Raccoon City Incident," which they will bring up again and again throughout the series.
RE3 is Jill Valentine's game, and also where the games begun to get a bit more bizarre, even for RE standards. This game introduces us to Nemesis, which still gives some players nightmares as he was an ongoing threat throughout the game.
Next you have the Code Veronica game, which elaborates more upon the Umbrella conspiracy with the Redfields. This is essentially the Umbrella game, where Wesker returns as a badass and you get more than a little bit acquainted with the Ashfords.
After Veronica, there was this long time where the RE series went into a gestation period, churning out games that mainly expanded upon the storyline, some for the better, some were better left forgotten. Although some of these came out during or shortly after this time, I suggest at least Resdient Evil: Zero
Then, lightning struck again with RE4. It returned Leon Kennedy to the forefront, but also pulled him away from the main Umbrella storyline into a whole new sidestory which, while ridiculous (evil monks, killer statues, giant salamanders), also breathed new life into the series. And also, any game you play that features 3rd-person over the shoulder camera mechanics (Dead Space, for example), you can thank this game for.
Afterwards, there was RE5, which was supposed to tie up all the loose ends with the Umbrella storyline, but despite its amazing production values, most people, myself included, think of it more as an action game than a horror game. Further, a lot of the characters we new from earlier in the series, specifically Chris and Jill, were re-imagined, one becoming Gears-of-War-Lite, and the other becoming a blonde Catwoman-wannabe. By and all, it IS a good game on surface value, but at the same time, for those who have invested their time into the previous games as well as appreciating the characters... let's just politely say it was a letdown.
So... take your pick. RE4 and RE5 will be the easiest to obtain, the others you might have to scrounge around for. I do know however they will be re-releasing Veronica in HD later on this year however on LIVE and PSN.
Happy hunting.
