The easiest way to handle the whole domain name/hosting/blogging issue is to (a) decide who your website hosting provider will be, and (b) purchase your domain name at the same place.
In case you are not familiar with the terminology, your website host is the company who provides a server that’s connected to the internet where your website files will be stored and viewed by anyone who goes to your website. Examples of web hosts are GoDaddy, Host Monster, DreamHost, Host Gator, etc.
Hosting service is now very competitive, and very similar. Expect to pay from $50 – $100 a year, depending on which provider you choose. The hosts that I suggest all offer similar services, very good support, simple WordPress setup via cPanel, and will host your email as well if you like.
I currently use DreamHost, so I will walk through the process of getting your domain there. The specific steps will vary from host to host, i.e. you will have different menus to choose from, etc but the process is virtually identical.
Be creative. I prefer to avoid intentional misspellings, although it works for some ( ). It should be as short as possible, memorable, something that’s easy to say since you’ll be using it all the time, and should be available with a .com extension.
Today, you are likely to have to use a phrase as your domain name, i.e. several words in succession with .com appended. Other top level domains like .net, .org, .us, etc. can work under some circumstances (e.g. .actor for an actor building a personal blog), but .com is the default that everyone knows so find a suitable .com domain if possible.
At Dreamhost, to buy a domain you need to go to this address. The first step is to enter the domain name you would like, to see if its available or if someone else has already purchased it.
A word of caution: I think every single word domain has now been purchased, as well as just about any short phrase you can think of. So what to do?
As you type the name in the domain name search box, Dreamhost is automatically searching all domain names. Those available and those already taken will appear and the search will return results similar to those shown above. The price shown is the cost per year to lease that domain name. You never actually own it, but you have exclusive rights to it as long as you pay the annual fee.