It's a tough call between Kain, Edge and Rydia for me. However, my reasons for loving them immediately are sort of shallow, as are my reasons for hesitating over which one to actually pick.
First of all, Kain. Kain's voice, which has been one of the only voices that ever came (shut up) close to being in the same league of my crushing adoration of James Earl Jones'. Spoiler alert: I have an enormous and somewhat inappropriate crush on people who can pitch their voices lower than the Marianas Trench reaches.
However, I'm going to agree with Sylvie that Kain exhausts the shapeshifter archetype more than the DC franchise exhausts the Lazarus pits. I do like that the degree of Golbez's mind control over him is left ambiguous in the sense he's always been envious of Cecil. However, it's irksome and loses some of its potency when he changes sides more frequently than you get to upgrade his armour (and we're talking an FF game, so that's like changing underwear). Also, I may well be shot for this, but the dragoon class, while amaze-balls and all, isn't my favourite class. That's the summoner one. Which brings me to...
Rydia. I watched the initial animation sequence and developed insta-crushes on Rydia and Edge. Rydia because she's a FOCKIN' BABE who can pull Dragons out of her bra. Also, is a FOCKIN' BABE. WITH GREEN HAIR. Who pulls it off. (Yeah, shallow).
However, I've never forgiven her for being about five years old when you first encounter her. The black/white magic thing was fabulous, although her lack of MP when you first start off is heartbreaking. I did find it in my heart to forgive her a little when she came back after being swallowed by a giant fish for half the game only to be as polygonally-mega-babely as one can really get.
Thirdly, Edge. This is the worst--my biggest anime crush of all time (goddon'tjudgeme) is Hatake Kakashi, to whom Edge bears a disturbing resemblance. Until he opens his mouth.
So it's really a tie between Kain and Rydia. I enjoy the complexity of Kain's character, hate Rydia's voice actor pretty much all the way through the game, but once you augment Rydia with MP+20% and Double-Cast, she's pretty much fucking unstoppable.
And she's the one I made my little avatar when I was world travelling. So I guess what I mean is--Rydia. Although Kain probably has the power to make me switching allegiances with as little hesitation as he does if I ever find my DS cartridge and hear his voice again.