When you decide to have your own hosted WordPress blog (an excellent idea) you need a few things.
1. A domain name. Choose this name carefully and whatever else you do, make it a .com name, not .biz, .org, .tv or any of the other extensions you will see. People are used to looking for .com domains. An excellent, easy and low cost domain registrar is The Wizard Domains.
Not only is it easy to get your domain, it is easy to point your domain to your new host when you get one. This company walks you through it step by step.
2. Excellent Hosting! The Wizard recommends Hostgator.
3. The Thesis theme - you will LOVE this theme.