This is what I think about the main games in the series:
FFI - Good game. I've seen the PSP version for $10 at Best Buy, and I definitely recommend it for that price.
FFII - Sucks ass. Skip it.
FFIII - Also sucks ass. Skip it.
FFIV - A classic RPG. One of the best ones in the series; I recommend the PSP version since it has all the FFIV games.
FFV - Solid gameplay, but average story. This game has one of the best job systems in the series, and I'd also recommend trying it out.
FFVI - Like IV, it's one of the best ones in the series. I particularly like how each character got their own screen time and side missions which fleshed out their character.
FFVII - It's good, but way overrated by the fanbase. The best thing about the game is that it has a lot of variety and optional content: snowboarding, chocobo racing, a RTS mini-game, Golden Saucer, etc.
FFVIII - Excluding the soundtrack, everything in this game is terrible. Avoid it.
FFIX - One of the best ones in the series. Beautiful world & artstyle, great story and it has Vivi!
FFX - Way overrated. Just watch the cutscenes on youtube. The gameplay sucks, and the encounter rate is so high that you get sucked into a battle after taking three steps. The sphere grid /level up gets a lot of praise for some reason, but it's actually a waste of time since the sphere grid is linear for like 75% of the game. They should just stayed with an ordinary level up system.
FFXII - This game gets a lot of hate, but to me, it's one of the best games in the series. Hell, it's one of the best RPGS I've played. Many people hate it because it's different than the others in the series, but this game needed to be made. This is a breath of fresh air and something that the stagant JRPG genre needed. Adjust the battle system to active and raise the battle speed, and it becomes incredibly fun (well for me at least). This game also has a lot of optional content and exploration.
FFXIII - Even though the game gets a lot of hate, I think it's pretty good. The combat is pretty fun. The bad part about the game is that there isn't much to do outside of battles.
To sum it up, start with either IX, VI, IV or XII.