FF8 was the one that got me into the 'new' ones (3D), absolutely loved it, and 9 was awesome as it took me back to the original games in style.
I say if you're short on time then choose between FFX and FFXII.
If you don't mind corridor style linear play, and you want an exotic new world and comforting soundtrack go for FFX.
If you want a more open world, a more traditional FF style setting (knights and stuff) and an exciting new battle system (with no 'cutaway' to battles, they're in the world) then go for FFXII.
(ok, you can see I'm a bit biased, but they're the main differences).