mayhaps, karl - I suck at jungle, so I'll leave that to you, but the early kill potential is higher anyway with tiger (that said, I'd play jungle udyr with phoenix as well for the fast clears).
Anywho... draven. I heart draven. I used to think he was rot, but now I love him as an adc. He has higher dmg potential than any adc early and he's the only adc that can peel for himself. Now, that won't save you from a good jungle gank, but it can give you a GIGANTIC advantage (above and beyond ANY other adc) late game. Here's why. And again, if you think I'm crazy, fine, but think about the following. The current holy trinity of adc's is ez, graves and corki. Why? #1 reason is an evade (dash/flash). After that, its any char that has a steroid (as/ad, etc). Corki doesn't have that like graves or ez. So, what does draven have? He has a steroid ability that can be cast every 2 seconds or so if he catches an axe. More importantly, he has an ability that displaces anyone attacking him (acting as a temp stun). This means if 2 characters dive for the back row, you can knock them away and keep attacking them. The main thing is that his ability typically keeps those enemies in range for him to hit (while ez/corki/graves as often out of position a little and cannot continue to attack). This means that with draven, you can continue to do more damage than other adc even after you would normally have had to flash away. So, ez/graves/corki are superior in that they can escape more easily, but draven is even better. He can escape easily because of his displace/steroid. he can also engage or stay in a fight more easily because of his displace/steroid. And he does more dmg than other adcs. So, I honestly think his potential is > than any other adc. It gets even better. No one bans him. Super. This means I can have ez banned out and reduce the champs that can go against me to graves/corki. Draven can out damage them as well. And last, riot will likely give a quality of life buff (this only matters for early game) to him in the form of the enemy not seeing that icon that shows where his axe will land.
Anyway - I draven. I'm not amazing with him yet, but I believe I'm slowly getting better and better. I feel more confident with him than any other adc currently at any rate.