Cait is a Carry. It means she sucks early game and pwns hard late game. The team has to carry her through the first part and then she can destroy opponents at the end. You're always gonna get targetted because if they don't then their team is dead. I crit late game for 1.5k on average, my crit rate is usually high 90s and I have just enough life steal to keep me in fights for a long time as long as I'm not targeted too hard.

Crit damage all day every day. A little speed to get a little speedy love. A little armor pen for a start. A little cool down to help with early game harass. Then it's all crit all day. I normally pop off 1.5k crits every hit every late game, which is about twice per second. I roll with about 40% crit damage. When I pop a crit on a headshot I melt faces.

21-0-9. You roll with the experience out of the utility tree to help you level faster. You roll with 21 offense to help increase your damage.

Avarice blade for the crit and gps.
Philosphers for the mp5 and gps.
Bloodthirster for ad and lifesteal.

Phantom for crit and as.
Infinity to hit like a truck.
Start selling the gps and go for what you need. Tank heavy= madreds. Karthus = veil. Another phantom always goes good. If you have a the cash rock a trinity.

Get all three. Max out Pilt for the harass. Trap to gankproof your lane. Then stack net to help you run (when you can't level peace).

Flash and Tele.

Flash usually to escape.
Tele to help you reach feed, backdoor, get loot quick early game.

Save peace for when you harass as well as minion hit.
Don't push too hard cause in lane you are the best farmer in the game. Push when you can. Take a sec to gank too. Your buddies will appreciate it.