Site Name
First you need to choose a name for your website or domain. It is recommended that your site name includes something about who are. "Fierce Websites" implies something to do with websites (as intended).
Be careful when choosing a name. Write it out how it will be displayed and maybe even ask someone else to look at it.
There have been many domain names which can be mistaken for other names. Not sure what I'm talking about? Take a look at these unfortunate domain names.
After you have decided on a website name, make sure it is available.
Web Host
What does a Web Host do? They get your web site online for you basically. Of course they do much more.
There are so many Web Host to choose from. If you want my opinion; I strongly recommend Lunarpages. They have many affordable hosting plans to meet your needs and support is great. Uptime is excellent. Nothing worse than having a server crash continually. Right now you receive $700 value in free software and bonuses.