I think to create image hosting website you need unlimited hosting package from any Good hosting provider like go daddy. What you have to learn about HOSTING to make image hosting website. According to me you should learn about how to make a file smaller on server (Compression), this would help you than learn hosting to create an image hosting website.
@mike2148 , it is much easier than you think. Just get a good hosting account with enough space and bandwidth. Then install a good image hosting script (Eg. http://codefuture.co.uk/projects/imagehost/ ) on your hosting. That's all you need to set up an image hosting website of your own.
Personally, I have tried only CF Image Hosting Script. But this link below gives a few alternatives as well http://alternativeto.net/software/cf-image-host/ PS : Of course, there are many paid alternatives as well