Which games in the series do I recommend.

FFIV
FFVI
FFIX
FFX
FFV

Those are my favorites. The following games haven't aged to well.

FFI
FFII
FFIII

And I just can't stand these games in the series.

FFVII
FFVIII
FFX-2

The only game I haven't listed is FFXII, the game is much different the rest of the series. Its not a bad game but I got bored with it 30 hours in and never touched it again. BTW FFXI is online more like a FF themed MMO than an actual Final Fantasy game.

You should play VI & VII definately (PS2 plays PS1 games)
IX is good too.

I haven't played the DS remakes but all SNES RPG's are great.

I would NOT play Crystal Chronicles on Cube and XII (horrible).

Most are good, but FFX could be a good starter, since it has voicework as a first in the series, it could more easily spur you into the FF universe (s).
FFVII is also good, as is FFIX, but FFVIII is probably the most varied in terms of gameplay (special combat system).
Of course, IV and VI are classics not to be foregone! If you can find them, that is...

You might want to hold off on FFIV, since the DS remake/port/director's edition will feature contents cut from the original game... apparently...

I wouldn't recommend you to start with IV since that is what I did.

I really like RPG's and was very much looking forward to play a SNES Final Fantasy, but I was very disappointed after playing it. I guess that it was great at its time, but if you are used to modern RPG's it's not that great. So I would recommend you to start with a newer one and if you like it, you can go back and experience the roots of the series.

Get 6 for your gba. Its the best ff imho.

Wait for 4 on the DS.
Then wait for 5 and see if you like it.
Wait for 6 DS and play the best (by far) FF game.
Also FF 9 is good.

Don't bother with the others, as FF 1-3 are too experimental and are not well balanced; FF 7, 8 and X are shit, FF XI is an MMO so it don't count. I haven't played FF XII, because I'm done with the main series.

I recommend FFVI,FFX and FFXII. Too bad that you dont want PS1 games because FFVII and FFIX are pretty good.

Hmm well if you think the FFs on PS are outdated, get FFX. It has voice acting, beautiful cinematics, nice battle system, great level up system (that permits you to chose how your characters level up) and it has the most fantastic story (it made me cry)!

FFVII has traditionally worked well as an introduction to the series, in fact for many people it was an introduction to both the series and RPGs in general. As a result I think it would be worth testing out. I know you didn't want people to name any PS1 titles but I figure if you say those are two dated then the SNES ones are well and truly dated and that only leaves you with a choice of FFX and FFXII.

Personally, whilst I enjoy the FF series I would simply skip it all together and go play Chrono Trigger.