You don't want to ask me that because I am so biased it is not even funny. But seriously, not even one of them? Damn. Hmm.
I'd recommend trying to find a copy of the original Resident Evil if you have a PS1 or PS2 that can still play PS1 games. Or, y'know, other means of playing PS1 games. >.> Director's Cut if you have to, but the new costumes suck ass and frankly I don't really like some of the puzzle changes or the fact you get like 2x ammo off every pick-up. It made the game way too easy, I mean, my brother for example is really good at those games and can get to the end with so much ammo and healing items... and I'm pretty good, I beat the last boss with 3 shotgun shells, 7 pistol bullets, and a knife. :3 I don't count the rocket since you have to use that to kill him. Anyway, once you're done with that, move on to RE2. It's probably my least favorite one but you should give it a try, you might like it, I dunno. I just don't have as fond memories of it as I do for RE1 and the later sequels. If you do play RE2 though you have to beat it I think 6 times to unlock everything. That game also has the introduction of HUNK, who's a fucking badass in my opinion... and yes, his name is all caps, that's not me being an ass about it. Anyway RE3 is pretty good, I haven't played it in a long time but I actually found my copy yesterday, and when I get done with my new Cv games I'm probably going to pop that in and see what's up with it again. RE4 is the game that everybody was shitting themselves over when it came out, and I'll admit to having run through it about twenty or thirty times - also known as a tenth of the amount of time I put in RE1 - but Leon's just not my favorite RE character, and the plot is, well... "Are you a bad enough dude to rescue the president's daughter?" His one-liners are terrible but funny too. The whole thing is like an 80's spy flick.
As for RE5, well, that seems to be something everyone's divided on. If you have a 360 and a gold account though, let me know and if you get a copy I can try to help you through it. Assuming I can borrow it from bro. >.> I like the campaign and the DLC but what a lot of people care about in that game is the Mercenaries mode, where you pick from three different versions of Chris and Sheva, or two different versions of Jill and Wesker, and try to keep a kill combo going to eliminate all 150 enemies as fast as possible. Wesker's kind of broken in this mode because he has an ability to 'dash', which knocks majini aside and counts as a melee attack. If you kill the enemies with a melee, you get 5 seconds on the clock, and there's some enemies that can only be melee'd by a dashing Wesker like the lickers and the reapers. As you might guess, I'm a Wesker player, but not a very good one compared to some of these guys. I'm like... lower-middle-tier, probably, and I rarely play Mercs anyway. My brother is awesome with S.T.A.R.S. Chris and is roughly the fourth or fifth best player of that character in the world, and it's a toss-up between him and BerserkerKev who is the best American S.T.A.R.S. Chris. If you wanted to play Mercs instead of the campaign I'd refer you to him. ^^
If you have a Gamecube, I'm pretty sure they released the first three REs on it (although not the original RE, just the REmake which I'm not a fan of >.>) and RE4 and Code Veronica are coming to Xbox Live Arcade soon, so there's that. I'm kind of torn about Operation Raccoon City which is coming out soon, I dunno about this whole squad-based thing being injected into RE2. I'll wait and see though.
Anyway, the thing with Resident Evil is that it's very cheesy. It's chockful of horrendous acting (except for RE5 and it's debatable about RE4) and ridiculous plots. If you're not the kind of guy who enjoys watching bad movies you might not like it.