[{quoted}](name=Master Fledgling,realm=NA,application-id=WEuoGbmp,discussion-id=nkEBRERP,comment-id=,timestamp=2015-05-13T03:48:54.547+0000)Initiate all by themself
Has reliable CC
Can build damage or tank
Has some mobility
Is not crazy mana hungry/is mana free at best
Bonus
Some sort of global presence/is mobile enough to help other lanes if needed
Very few supports have mobility. The most mobile supports currently are Braum, Bard, Naut, and Janna (with her passives). However, Janna is not great at initiating, Braum is not that great if you build damage on him, and Bard is far from reliable. Naut has good CC, initiation, and mobility, while being a tiny bit mana hungry and should be built tank primarily. Lissandra is a niche-pick support; though, she has mobility and CC, and she can be built tank or damage.
Lots of people are recommending Soraka for her global presence, but she is bad at initiating, does not have reliable CC, is not built well with tank or damage IMO (she's built better with utility), and is not very mobile. She is the only support with global presence, though.
Leona, Thresh, and Annie are some of the best initiators with hard CC. However, they are not mobile, and while Annie can be built tank or damage, Leona and Thresh are both optimally built tanky. (You can do a cool trick with Thresh' hook to give you some mobility by hooking jungle camps to escape, but other than that he is pretty immobile). Morg has good CC, and her snare and ult are great initiation tools, but often it is better to save them for peels.
The most mana hungry supports are Nami, Lulu, and Sona in my experience.
Just laying out all of my thoughts; hope they help! :)
EDIT: Completely forgot about Blitz. His hook is probably the most broken form of CC in the game, he can actually be built either tank or damage (whether AD or AP), his mobility got nerfed (cry me a river, Blitz players), and has a tonne of presence with his hook. Even though he is mana hungry if he misses abilities or spams, if you land hook once or twice on a squishy target within a 5 minute time-frame, you have an almost guaranteed kill on that target. And, even though he does not have a global ability, sometimes just walking into mid lane can make the enemy mid laner blow their flash.
**Overall, I'd say your best options are Liss, Naut, and Blitz based on your criteria. **