When i play Caitlyn I usually start out with a Doran's Blade Then when in Laning Phase you should wait till Level 7 to engage in a teamfight at botlane. I get Bloodthirster for my first item because when your passive comes on it gives you a lot of health just with a passive hit. I go for a Phantom Dancer after Bloodthirster because with the attack speed and Bloodthirster combined you get ALOT of health. I get Infinity Edge after Phantom Dancer because you need some damage output so that will be your damage source. After you get your Infinity Edge i like to get last whisperer cause that's when all the tanks on the enemy team get health and you usually need to group up to take out the tanks. After you get Armor Penetration I would probably go for Frozen Mallet because it gives you damage plus some health to keep you alive.