Let's see if I can answer what Dae has asked of me.
Characters: I'm going to split this answer into Heroes, Villains, and Gilgamesh.
Heroes: First of all, everyone in FFIX. Absolutely every character. Especially Zidane. Dissidia has made me like Firion a lot. Bartz is another favorite. I'm also fond of Locke, Edgar, and Setzer from FF6, as well as Cait Sith and Yuffie from FF7, and I also like Vincent but only in the sense that with him, Cait, Yuffie, and Vincent would make a fantastic Comic Trio. Zell and Selphie are also the only likable characters I've seen in FFVIII, although maybe actually playing that game would help me.
Villains: My top three villains in all of Final Fantasy are Kefka, Kuja, and Exdeath, although if I had to pick one number 1 favorite, it'd be Exdeath. I also like Zorn and Thorn from FFIX if we count "side-villains", because they're so much fun to hate, and I love the whole "twin character" dynamic. All of a sudden I realize it'd be awesome to have a fic where Palom and Porom have to fight Zorn and Thorn.
Gilgamesh: Yes.
Story: Out of the ones I've played far enough in to know, I think V and IX are going to have to win this, because those are the two that felt the most consistent to me and they're the ones that kept me ready to see what happened next.
Music: This is actually very hard to answer because all Final Fantasy games have excellent music. FFV has some really amazing tunes such as Clash on the Big Bridge, The Dawn Warriors, The Decisive Battle, Neo Exdeath, and the map themes. Although for overall best music, I think I'll have to give the nod to IX, because it feels very "complete" and has even more amazing tracks than V (Over That Hill, Aboard the Hilda Garde, Vamo'Alla Flamenco, Hunter's Chance, Jesters of the Moonless Sky, Rose of May, Dark Messenger, The Final Battle/Grand Cross, and of course, Melodies of Life, which I will be singing to myself until the end of time).
Visual: You know, I really wish I could find one of these I could say something other than V or IX for. I love IX's "cartoony Renaissance" visual style, and V does a good job of stretching 16-bit graphics across wide, sunny plains, mysterious cloudy lands, dark haunted ships, ancient temples and caves, and even more.
Battle system: This one's a bit harder for me to answer because I rarely notice differences in the battle systems. I think I'd need to play more games side-by-side and back to back to answer this one. I hear X-2 has a really fun battle system, though, so I'm looking forward to trying that out. Hey, does Dissidia count?
It's hard for me to answer these questions unbiased because I've only beaten I, V, and IX and those are the ones where my expertise lies. I've not gotten very far in II or III, I've gotten near the end of IV but never beat it, I'm working my way through VI, I only got past the first disc of VII, I only got past the first ten MINUTES of VIII, and I forget where I got bored of X. I've also never played XII. I'm working on replaying (or playing in some cases) all the games, though.
