So basically I just became an *** about people playing Caitlyn the way I think is pretty bad. People will probably scream at me for this, but whatever: This build focuses on sniping your opponents, nothing more. If you prefer going other ways with Caitlyn, be my guest. But this is how I build her, and if you're interested you stay and read.

My basic thoughts are: DAMAGE!!!!
Basically.

I never saw Caitlyn as a champion who you go in and auto-attack with to get kills. And I never will. All I do with her is do sniping, be it with a Piltover Peacemaker or an Ace in the Hole Therefore I love early Attack Damage, since a clean shot from the Peacemaker at leve 2 removes more than a 100 damage from your enemy.

However, I have never had a good experience against Ability Power characcters; That's why I use Magic Resist per level Glyphs, to go against that (to a certain degree).

21/0/9. I don't see any wierd stuff there. Plainly there to dish out heckloads of damage and nothing more. Taking extra mana and mana regeneration can be good however, if you are one of those "Sir Spamalot". And even if you aren't you can't rely on having a Soraka in your team or someone having Clarity in your team to lane with you all the time. And picking Clarity yourself is only waste of space.

As I have been saying, I do NOT focus on auto-attacks to win. I always focus on sniping my enemies, no matter how much hp they have. It might sometimes come down to a Madred's Bloodrazor if I meet something like a Volibear AND a Garen, but otherwise it's usually enough with only Damage. The Piltover Peacemaker does at least 1000 damage when you've reached full build, and Ace in the Hole can probably one-hit Teemo in the enemy team.

Focusing Piltover Peacemaker, no wierdies there.

Now here comes the part where many people probably think I'm mad. But the reason I prioritize 90 Caliber Net is because the cooldown on that at max level is ohnly 10 seconds. I want a good chance of escaping or chasing, and it's far more reliable if the cooldown is low. Usually people want Yordle Snap Trap instead, but I don't. The only thing that happens is lowered cooldown and increased damage (which I might add is very low). The immobilizing and sight effects are both still the same, so I think that since you don't usually use it in the heat of battle, it's fairly unnecessary to level it up.

As a side-note, I usually forget I have traps ;P

Usually I use Exhaust and Ghost. Alternatives can be using Flash, Cleanse and Ignite, if any of those suit you better.

Exhaust: for escaping and chasing purposes.
Ghost: same reasons.
The other spells: Ignite is a good finish-off, Cleanse is wonderful if the enemy decides lots of cc is good, and Flash has always been a great spell.