I started my adsense with free hosting. I had success before with free hosting. I was using 50webs.com free hosting plan. I used it for two subdomains like subdomain.50webs.com and I was very satisfied with it. Later I purchased domain names and hosting.
why you do not purchasing your owner website? it not cost too much, you can get the whole thing here. http://www.myinnet.com
I there's something weird with dreaming of making it big with adsense yet being unable to pay 10$/month for hosting a real web site. Is it so horrible to invest a few dollars?