Hello! I'm new to LoL and am working on learning my first champion, Tristana. I got her from following the game on Facebook, which is where I heard about it to begin with. I've played a couple of games and I have a question. Is Attack Damage or Ability Power better for Tristana?

I have gone Attack Damage for my first two games and it's worked well. I level Rapid Fire first so that when I have high attack damage items I can get big hits off quickly. Rocket Jump is my secondary ability, as it serves both as a great gank tool and as an escape. I level explosive shot when I can't train either of the other two, with my ultimate taking priority over all else of course.

Is this the correct way of playing, or should I be training a different skill order and/or going AP?

I think it's a matter of taste, and also about how long the game will last. If you have a level advantage with Tristana, Rocket Jump will do plenty early. If you manage to snowball well enough, then your damage output will always be decent enough to at least Rocket Jump -> Buster Shot -> Rocket Jump. One of the issues is that you don't have enough throughput (all of Tristana's cooldowns are relatively high, so Lich Bane doesn't work well on her either), and in general your Rapid Fire is going to waste.

AD, however, is a little safer. You take advantage of your first skill as well as your passive, use Rocket Jump as an escape, and use Buster Shot as disruption.