When I looked at various hosting sites a while back, none of them (including Flickr and Photobucket) really offered what you want (unlimited upload, no limit on photo size) for free. I started out with free Flickr account, went to Flickr Pro, then recently started using SmugMug after the big, fat fail of a interface change at Flickr.
Bit dated now, but here's a thread on photo hosting.
http://www.head-case.org/forums/goredwings19s-computer-help-hotline/6022-photo-hosting.html