I wrote a blog recently on how to build a cheap web site – really based on using a blog as your web site.
I’ve looked further into this option and into using the domain name for your blog. You can do this one of two ways:

First, you could register the domain name with a registrar, such as Go Daddy. You can set up your email with Go Daddy. Also they will forward you domain to your blog. So when someone types in http://www.yourdomain.com it will go to your blog, which might have an address like yourname.wordpress.com. But once you visit that site, the address in the address bar will look like the WordPress address, not the domain name.

One small way to change this would be to have Go Daddy mask the domain. Then when someone visits the blog, they will see your domain name – but as they browse your site that address won’t change. So that the address on the About page (for example) would still look like: http://www.yourdomain.com not http://www.yourdomain.com/about.html. It makes it hard for a visitor to point to a specific blog post.

The second option is to map the domain name through WordPress. You can do this by going to your blog dashboard and selecting Upgrade in the menu. Then you’ll see an option for domains. You need to buy credits (I think it’s $15) but once you do you can point your domain name to the blog and the site will reflect your domain name on each page.

Now you can also set up email through Google Apps. Here’s an article that outlines that process: http://faq.wordpress.com/2007/05/23/gmail-mx/