I've used godaddy, and i've not used but heard good things about 1&1 and host gator. If i had the money, i'd use
mediatemple. But most the websites that people are suggesting are very known and reliable. But i'd reckamend you'd put a little more description of what you want the hosting for because html and lots of memory/space is not something you really put together. Most non-free sites are not free because they are offering php/asp.net/linux/etc. You could probably get a free domain and host for the html, and use a free dns forwarding to host the big files on your own computer/sever.
(Also, if your using a database, my personal luck with godaddy has been fine (MSSQL and MySQL), but it could depend on time zones, and the way your database is set up. Customer service was excellent to, i broke one of their databases and they fixed it within 2 days. hehe
