Well, this is my first build so constructive criticism is useful, but anyways since Caitlyn is free this week I decided to try her out. She's really good at farming minions, dealing tons of damage while, if you're smart, taking hardly any. Most my games with her with this build usually are positive unless the teamwork is just horrid.
Welcome to my build!

One of the reasons Piltover is known as the City of Progress is because it has an extraordinarily low crime rate. This hasn't always been the case; brigands and thieves of all sorts used to find the city-state an ideal mark for plunder, primarily due to the valuable resources it imports to fuel its techmaturgical research. Some even theorize that it would have fallen long ago to the chaos of organized crime if not for Caitlyn, the Sheriff of Piltover. Born the daughter of a wealthy statesman and a pioneering hextech researcher, Caitlyn discovered her natural gift for investigation when, at age 14, her father was assaulted and robbed on his way home. She snuck out of her house that night with her father's rifle and tracked down the muggers from the crime scene. At first, her parents did their best to discourage her from such risky hobbies, but she was incorrigible. Wishing to protect her daughter in the only way she knew how, Caitlyn's mother began outfitting her with techmaturgical devices tailored to her sleuthing needs.

Caitlyn quickly gained notoriety, both because she was single handedly defeating crime in Piltover and also because she soon developed into a ravishing beauty. She never backed down from a case or a challenge, and she was one of the sharpest shots in the city-state. Her services were soon requested by Demacia to help track down a mysterious outlaw who had begun committing high-profile heists. The bandit, who always left a card with an ornate 'C' at the scene of the crime, became Caitlyn's arch-nemesis. To this day, Caitlyn still searches for this cat burglar, and the chase has led her all across Valoran. She has joined the League to hone her skills and gain the influence necessary to track down the only quarry that has managed to evade her.

''Go ahead, run. I'll give you a five minute head start.''
- Caitlyn, from her book 'Willing Apprehension'.

I really don't have any so I would go with Marks of Desolation, Seals of Vitality, Glyphs of Focus and Quintessences of Strength, just my opinion on it. You don't have to use those runes since I'm not using said runes.

21/0/9 Havoc is a must! More damage, more kills. More kills, more gold, so on and so forth.
MUST get Havoc no matter what.

Now, here's what I've been waiting for. I start of with Boots of Speed 2 Health Potions and a Mana Potion. If you mid you'll use the mana pot and the health pots if you take some damage while harassing. Then I usually go for, a Yomuu's Ghostblade for the damage and armor pen early on.
Then after that I go for The Black Cleaver. Since the on hit effects are just amazing. After TBC I go for Infinity Edge for the AD and the passive.
After IE I go for Bloodthirster, for the AD and the Life steal. After that (if I need to) I'll get a Phantom Dancer (don't know how to upload images)
This build is expensive! Try not to die too much, but try farming as much as possible since 20 minion kills is worth one champion kill. :P

My standard summoner spells for ALL champs are Ignite and Flash nowadays. Flash to get out of a tough situation, and ignite if you're chasing someone really low on HP. (Ult helps here too!)
I dunno what else is good with Caitlyn but having her 90 Caliber Net and Flash is a must for escaping.

I usually max Piltover Peacemaker first due to the AoE and the massive damage output it does. I pick up Yordle Snap Trap after at lvl 3 then 90 Caliber Net at 4. Maxing Q is a must for me. Ace in the Hole (ult) when you can! 90 Caliber Net last due to the weak damage.

One of the best farmers in the game, imo. With Infinity Edge, Black Cleaver, and Bloodthirster.
I usually crit around say, 1400 on minions, about the same on champs with no armor. I usually end up with 150+ minion kills at the end of the game.

TL;DR. This build should own people if you know how to use Caitlyn, and calls for expensive items, but farming minions and champions should make it a lot easier on you. I'm not gonna do a exceedingly long summary for this. If you don't wanna try it, then don't.
Gl, and HF with my build!

I dunno how to upload the images, and I'm on a time limit so I can't figure it out right now, if someone would be willing to tell me how, much would be appreciated.