Any of them, really!

Well I definitly reccommend VIII and IX. And then XII and X. Well thats the order I think from best to not the best, but still very awesome. Some people find XIIs quality debatable...But I still love the game.
VII and VI are also usually highly recommended by people. I wouldn't know though as I havent really played them.

It will all depend on what type of RPGs have you played in the past and what you like best. Final Fantasy games have tended to evolve with every iteration.

Story wise the earlier ones are the weakest (1,2,3). XII has the most politics and most interesting story (IMHO) as it was made by the TACTICS team (creators of some of the best RPG games ogre tactics, ogre battles and of course Final Fantasy Tactics). XII and Tactics are in the same universe (shared with FFTA for GBA and FFTA2 for DS as well as Vagrant story for the PS1) which is a first for the
series.

Gameplay wise, while tehy are called turn based RPGs FF has evolved overtime to be "less" turn based (called Active time battle system or Charged time battle system). I was not a big fond of them as it requires a lot faster hand eye co-ordination than my SRPG loving hands can keep up with. Half the times all of my characters would be ready to execute commands and I would still be fiddling with menus for the first one.

XII does it the best IMHO since now you only control one person (others are controlled via AI that you set). Gambit system evolves as you progress through the story and is pretty neat.

IF you are a fan of Grandia or to a little extent star ocean you will like XII better. although i do believe Grandia's battle system is the best considering its a mix of real-time AND turn-based (battle pauses while you are making decisions and it is really fast paced)

In terms of Epic scale the "final" in final fantasy is all about scale. The stories generally span multiple kingdoms, different ideology, politics and war (notable exception being VIII which has a more central Love story).

The only one of the series I haven't played is IX (although I own it). I just haven't gotten around to playing it.

Graphically, XII looks best and X and X-2 are close second. Cut scenes in all of those look phenomenal especially on a PS3.

X has an interesting levelling system which I really liked as you are not levelling all stats at the same time just one or a couple at a time. The battle system requires a little bit of strategy but it is pretty simple (rock paper scissors kind).

SO, depending on what you have liked in the past and what you enjoy most following would be my recommendations.

- epic scale of Story
VI, X, XII

- Love story central to the game
VII, VIII

- Graphics
XII, X

- Innovative battle mechanics
XII

- Memorable Villains
VII, VIII, X

- Memorable Main characters
VI, IV

- Music
very subjective but almost all of them have amazing sound tracks my favorite is X but I have played it the most. VI is very popular too

- Length of quest
If you have played and liked most tales games and like really long games X and XII have tons of side quests

If you are patient and like Strategy role playing games pick up FFT: war of the lions for the PSP from Amazon today AWESOME game and a bargain

FFX is the best starting point IMO

Do:

IV: DS
VI: Any platform

VII to X PS3 (you have BC I suppose)

Don't:

The rest, instead try Chrono Trigger, Xenogears, Suikoden.

Soriku I will fight you to the death over this

I liked VII and VIII the best.