In the meantime, you can use this site to look for an available domain name that you like:
They're a good place to register a domain... it costs $9.95 a year and they include private registration with that (personal details are hidden that way).
Feel free to register a name if you find one you like, just be sure to *not* add any hosting options. That makes it more expensive, and you may not need that. If you have any trouble finding a name that you like that is available, consider looking at the .org addresses in addition to the .com ones.
From there we can talk about what you want on the website, and how you would like to interact with it, but all of that happens after you have a name picked out. Let me know if you have any questions in the mean time.