Afaik, such a site already exists:

http://www.princes-horror-central.com/allclips.htm

It doesn't really have any view online support though. The site is kind of clunky but it does the job if you ask me.

If you still want to make this site, here's my 2 cents:
As far as hosting such a site, it wouldn't really require more than a PC with a decent CPU and 10TB of storage. Bandwidth would be the bigger issue here... and also the upcoming EU copyright shit.
If I were you I'd probably look for a more professional (but costlier) option in Romania (best internet for the price and usually unlimited bandwidth - I get over 950 Mbits download and 450Mbits upload for under $10) , Hungary or Russia.