what is the process of getting a domain name registered of your choice ?

[Jake]

Any of the countless domain name registrars can set you up with a .com name, godaddy is a popular one that sponsors a stock car racer, and had scantily clad women ion commercials (don't know what that does for your web site) typically the price is about $12 a year, look for new domain name discount coupon codes or other incentives (you should always use a godaddy code like from retailmenot.com)

Normally your registration details is publicly available through a whois query service, there are pair "privacy" proxies who keep your address and phone number concealed.

Email services provided by a registrar may vary, this may be more import if you want to start using it for email before you have a host and site.

All of the best .com names are already taken, be prepared to employ your creativity to come up with a compromise name that's available. Some registrars provide bulk search tools so you can check a list of names at a time:
http://www.godaddy.com/bulk-domain-search.aspx