NB! This build is pretty outdated now, I haven't really looked at it in a while. I hope people still like it, and have adapted it to your needs, but I really basically stopped playing.

All of his moves stack with Ability Power, so it only makes sense to build it on him. However, he is an auto-attacker as well, so some AD is definitely necessary, and I think that's why pure AP builds don't work very well.zzz

These are the summoner spells I find myself most often using, although I almost always use flash and exhaust.

Flash is perfect for escaping through walls, flashing to get off that extra leap, just an all around good summoner spell.

Well I hope this helps all the Jax's out there. Play smart, and you can kill the Lord Ruler himself. I absolutely adore getting feedback.