A good free website editor is
Kompozer, but it does require you to create individual pages i.e. it's not a "site creator". However, if I'm reading the Webs site rightly, it looks like they have their own Templates that you can use directly, so you probably don't need to go looking for anything else.
How much storage is "lots"? I have a free account on
wordpress.com, which is good for simple pages and blog-type journals. It now has 3GB of disk space as standard, but only certain file types are permitted i.e. documents and graphics, not MP3 files or programs. You can pay to remove those restrictions and get more space.
Edit : poking around, I see
Google Sites is offering 10GB of space at no cost, page creation, and some other bits like Google Apps and Calendar. I have no experience with them, however.