As well, if you want a complete list of weapon customizations, go to the FFX section on the frontpage of this site.

I'm actually doing something similar to you now. Except I've already got Caladbolg (the Chocobo Race isn't that bad, I completed after a while), rather I'm trying to get good AP gaining weapons.

So I've been told in another thread just yesterday to defeat One-Eye in the Monster arena, which drops weapons with Triple AP and 2 or 3 extra slots. Get one of those, and add break damage, triple overdrive (which you can get from 30 winning formula, which I"m pretty sure you can get in the Monster Arena), and Overdrive --> AP (which you can get from 10 Door to Tomorrow, which in turn you get in the monster arena), and you've got yourself one mean weapon. You'll advance around the sphere in no time, and create incredibally overpowered characters.

But really, I suggest trying the chocobo race to get the Sun Sigil so you can power up Caladbolg. Worst case, it'll take you an hour, at the very most to win it. Probably less.