There's no such thing as unlimited hosting. Anything that's advertised as unlimited is either a) oversold so it'll be crappy or will become crappy eventually b) unlimited but only for trivial/personal use, and limited by the ToS or c) is unlimited but reserve the right to kick you off if your usage disrupts anyone else, which it will if you see any non-trivial usage.
The question is is how much bandwidth to you currently use for videos? If you don't actually use very much you could probably get away with using an advertised unlimited hosting plan; if it's not much actually used they may not notice you.
If you do get heavy usage for the videos, then it's best to go with something a little more $$ but that actually can deliver what they say and won't remove you if you use a lot.
Something like these guys might be a good place to start:
http://www.webhostingtalk.com/showthread.php?t=1070823
But it really does depend on how much bandwidth you currently use.