co.cc is unprofessional. makes you look "fly-by-night"
people are going to trust you with their computers, computers are expensive, something that most don't get all that often, and things that people put a lot of sensitive data on.
pay for a .com or a .us site name, don't loose out on a potential customer or sale for the sake of a few dollars on domain registration.
also try not to get a free hosting site that adds loads of adverts or anything.
your site is likely going to be really low traffic, so hosting from home is a realistic option.
At a push, you could set up a site on blogger, style the page to look like a website rather than a blog and have traffic hitting your domain name resolve there instead.