Good, cheap hosts are pretty easy to come by. PM me if you would like a recommendation.
If you get a domain name, I highly recommend that you purchase it yourself. Do NOT let your Web host purchase it for you. I have seen messy disputes over who actually owns the domain. A hostee tries to leave the host, but the host won't transfer the name rights to the hostee. It's better to have total ownership of the domain so that you can change hosts whenever you want. For domain registration/administration, I highly recommend GoDaddy Software:
http://www.godaddy.com.