I advise you to play IV and its two expansion The Lose and Damned and The ballad of Gay Tony before the others, as it's in the same universe as V and you'll get to see a few of the characters, specifically Packie Mcreary and Johnny Klebitz. Its actually a very good game regardless of what some say on here, I feel that although it lacked some of the awesome free roaming and customization features of San Andreas it made up for with its story, I really enjoyed the story and it's characters; it was consistent, which can't be said for San Andreas' story in all honesty.
The biggest reason people prefer San Andreas and Vice City is for nostalgia reasons. In fact, dare I say it, you may not get into those earlier games now as you would have done 8 or 10 years ago.
Saying that, my favourite GTA was Vice City, loved the era, the music, the story. Was awesome. San Andreas was really good too.
Graphically they're still pretty good I feel, though again it may be hard to get into them now more so that you don't have that nostalgia motivation, as much as I'm not a graphics whore it was hard to me for a little while to really get past the textures and start enjoying the game. You get spoilt with today's graphics I guess. The biggest leap though is going back to the actual gameplay in terms of shooting and stuff, it's quite "clunky"... hard to explain but if you;ve played them you'll know what I mean, it gets easier each game progresses, with San Andreas being a cake walk compared to III.