If Free Domain hosting is not for you!! Then expand your search to more web hosting services.
HostIndex.com - is one of web's largest hosting directory. User can search through hundreds of hosting companies, learn about hosting information, and read tips about hosting services.

Register your domain with Network Solutions
Network Solutions is a company that maintains the records of all domain names. If you register a new domain name, Network Solutions will bill you $70 for the first two years and then thirty-five dollar per year afterward. These free web hosting services is not in anyway affiliated with Network Solutions and has no control of their charge. It's hard to register a domain yourself if you have no knowledge about domain names. I suggest using a Free Domain registration Service. Note: Be careful of any web hosting service whom offers you free of the domain registration fee. I have not included any of them because these service are likely to register your desired domain name for you, but under their name and therefore blocking you out of your domain if you ever want to change hosting companies and allowing them to charge you any amount they wish later on if you wish to keep the domain. Which means you can't be the Master of your Domain.

Note: After you register your domain you then need to park it somewhere temporary. Park it at AO Soft - Free Domain Parking.   It's free of course. Other places charges you $25-50 dollar. If you want they also register your domain for you for free.