My favorite ADC in the past has been Miss Fortune for her crazy strong early game, and excellent AoE team fight damage. She is also extremely good at chasing down kills with strut and her Q.
However, lately I have been playing Tristana again and she is still an amazing carry. Lategame it's pretty unquestioned that she has one of the best carry potentials, but her early game is also very strong compared to other ADC, assuming you prioritize W and E for spell leveling.
She is definitely not a strong poke champ in early game in the traditional sense. You can try exchanging pokes with her E, but it is usually a waste of mana. Her autoattack range is fairly average at the start of the game, so you will be taking auto attack hits and buckshots/etc often and you will generally lose the exchange if you try to out poke them.
However, if you put all your points into W and E without any in Q, your early game burst is crazy good. If your support can land a CC on their carry, you can generally jump in + E + ignite and it will be an easy kill, with a chance to get their support too because of the refreshed jump's slow.
As others have said, her one weird point is transitioning from early to late game, where your burst from WE is not enough to kill and your autoattack damage isn't amazing yet. Getting an early game lead is pretty easy, so this usually isn't too bad, but it can be rough when matches are slow farm fests when you hit mid game.
Some useful tips that I live by:
1) Max WE without any points in Q is best until you get your IE, then put all points into Q to dominate early game and then a quicker transition to late game, usually this will leave you with maxed W and 2 points in E before you start maxing Q.
2) In team fights later, just autoattack and save R for a melee that is on your face, and jumps to get to keep some distance (even against other ranged this can be very useful since you outrange most). Once a few of them die, then it is generally safe to rocket jump into the fray.
3) Standard ADC build/runes/masteries work well on her. BUT I actually prefer masteries of 9/0/21. Starting with a doran's blade and a health pot and a biscuit is very useful when they want to trade pokes. The utility tree is surprisingly potent this season, and the extra movespeed, lifesteal, CD, experience, and gold generation from pickpocket and greed are all much more useful to me than the bit of extra damage in the offense tree.