FF isn't multiplayer, though Final Fantasy XI is an MMORPG, so that the only multiplayer you can get.
Final Fantasy VI, VII, VIII and IX were the best in my opinion, very strong plotline, fun to play and always had something there to keep you going. They were also quite stylistic. VII being my all time favourite (Though people say it's over rated, but I love it).
The ones before VI are also very good, not my favourites, but are good 2D classics to play with once you get into them.
Final Fantasy X is good, a good take on for the PS2, new great game play features and it was great fun, though they removed their 'I can walk on the world map' feature. It still follows the same sort of thing as the previous.
Final Fantasy X-2 - keep away from the game, it is horrible - it's what my friend has label 'softcore', it pretty much contists of 3 tarts chasing around in skimpy clothes and not being any good. More or less annoying.
Final Fantasy XI - Not played it, I hear it's very good. It's an MMORPG
Final Fantasy XII - Where's Darth Vader when you need him? The plotline very conveniently manages to mimic Star Wars. New game play, quite cool, interesting characters and ideas and it seemed to imitate the MMORPG style (to make up for those who didn't want to pay monthly for FFXI)though being single player. The annoyance with was - Yey! Plot, interesting stuff, it's going along, great, now my characters are too weak, 3 hours of training, yay, continue plot, nice boss, good bit of fun, damn character now too weak, 3 hours of training them...47hours into the game and I still don't feel very far.
Final Fantasy: Crystal Chronicles - something a bit different, a bit more medieval and childish, but good fun never the less - you have a less turn based game play and you can have up to 4 players, so that's always good.
Final Fantasy: Tactics
Great game, but the only interaction is the battles and the gameplay for that is well...you have got to set out the tactics for them in order to fight and win. Good fun, plot is also good, as it was made during the time Square had hotpot of great ideas.
Final Fantasy: Tactics Advanced
Like the above, but for the Gameboy Advanced - good fun completely different plot, and more childish.
There are still many other Final Fantasys out there, I'd love to talk about them all in depth, but that should be a good starting point.
"Experience never provides its judgments with true or strict universality; but only (through induction) with assumed and comparative universality." - Immanuel Kant