most wil as mdrafi said, if you are just starting out, get a small package, 1-5gb space that's NOT oversold, you should be fine, also you can ask around hosts and see if they allow it.
Most shared hosting companies will not let you run image hosting scripts on your site... you'll want to consider a VPS or dedicated server at the minimum...
We allow anything legal in the USA on our VPS servers, as most VPS providers will, since our's aren't oversold. This includes proxies, image/file hosting, etc..... Check out xenvds.net
Well i have dedicated servers that would allow that,and i have shared hosting with image hosting allowed,but u will not get speeds more than 500KB/s(4mbps),if you want this contact me and we will make deal!
A lot of shared hosts also do allow it but quickly suspend your site if you're overusing resources. That makes it somewhat hard to tell because they might say you may host image hosting but then there's some other reason that would hold you back.
A VPS is always the best option regardless of what you are hosting, this is because of the fact that you can make your VPS entirely the way you want instead of relying on some "default" server settings. In your case it would be to tweak the VPS so it's made for image hosting with alot of visitors viewing images only.
I highly doubt you will find any reputable hosting service that is going to allow what you want in a shared hosting environment. What you need is a dedicated server. The reason hosting providers do not allow image hosting scripts on their servers is because they are way too resource intensive and tend to affect other sites on the server negatively.
Er, well.. You'll find that those are in the same category as the image hosting scripts. Proxy sites belong on dedicated servers as well. They are just way too resource intensive for a shared environment.
I am allowing Image Hosting Check my thread and tell me if you are interested. I definitely allow MIH Script. http://forums.digitalpoint.com/showthread.php?t=1233072