Until now, Earth has been the most common choice for Kira that I've seen. Recently, people have been using fire well, also. It seems like Kira would benefit greatly by the added armor that water offers, but in practice I think she would never really get a chance to call out the ice spheres to begin with.
Earth gets the nod from me, at least until I see more. It's what I'd use. Neither arcana is very useful for Kira in mid-screen combos, but both can be put to good use when you're by the wall, and Kira tends to get people over there pretty fast when she can land a hit. You've probably seen it in videos already, but...
Fire gets more hits and damage against the wall, just because of the extra hits from the arcana super, but Earth isn't far behind. Fire gives you some worthwhile projectiles, a useful attack after guard cancels (the burst super), and normal homing cancels and guard cancels.
Earth is very useful for Kira when it's activated, because the super armor is useful and she can combo into the arcana force. The rock fist is pretty good at mid-range, and Kira can sometimes use the boulder, too. The stomp super is a good surprise move if you've got meter to burn or if your opponent is keeping you away. And Earth's homing and guard cancels are kind of crap, but they work just fine for Kira.
I saw people use Lightning with her a little bit when the game was new. It's a good distance attack against people who are just sitting around throwing projectiles, but that's all you can say for it. Kira doesn't get many knock-downs, so lightning & dark setups don't seem very good for her.
Oh, and time - I think it's probably not actually a very good choice, but it's the only arcana that can let Kira actually move fast. Dash behind -> 360 throw (KSB?) is pretty scary if you have the spacing down (and they aren't always jumping). However, Kira's back dash is really short, so the arcana doesn't seem to help much there.
EDIT: Uh, that's just my opinion, though. I suck at this game.