1st get the domain.  You will pay about $10 for the year. That's it.  Don't spend any more! (unless it's to me ;)
I use http://mydomain.com but godaddy, enom, or any of those will do.  You can wait and get your domain via Google when you sign up for Google Apps this makes some things easier like adding a Cname listing for new sites but you also want to have other domain management tools you can use. See more about set up here.
In choosing the domain hosting, pick one that has domain management tools plus URL forwarding. You don't need email from the domain host if you are going to use Google. Keep in mind that the domain is just a listing.  It's like getting your name into the phone book. It doesn't mean you have any web space just like the listing in the phone book doesn't give you a phone.  That's fine though. Don't be fooled into thinking it's only a "real domain" if it's packaged with web hosting.  Your domain is no less real than a phone listing that you didn't pay the phone company for. 

Now for the web hosting.  You can pay big bucks for an account that you can FTP to or even small bucks, like $5 per month, for a template kind of site that you get easy to use tools to build your site.  But if you are going to have to do a little work yourself anyway why pay anything?  I say go with free and see if you like it.  That's why I use Google Apps.  It's sort of a template type web site hosting with a whole lot of tools, like email, calendar, and documents, and a whole lot of flexibility.  Now before you get to thinking I get a kick back from Google, it seems that they don't even want people to know about the free version of this stuff.  Unless you search for it, you won't find it, but I'll give you the link: http://www.google.com/a/cpanel/domain/new is where you can sign up for what's called the standard edition of Google Apps.
Once you sign up you can then begin to set up things by following the instructions including verifying your domain.

They also have a step by step guide to setting up your new Google Apps account but some of it is directed toward the "premier accounts" or education and non-profit.

Now make you web page.  Two easy choices are Google Sites (part of the Google Apps suite) or you may want to try Blogger.com. Google Sites is a pretty extensive web site development tool with free hosting and plenty of gadgets but Blogger, (also owned by Google) is a slightly simpler and maybe slicker web site creation tool that has some ready to go networking features already built in such as multiple ways to create posts and the ability to easy link your posts to facebook and other social sites.  See PeninsulaTeaParty.org for a site that is a combination of both Google Sites and Blogger pages. 

Either way you go you will want to make your domain point directly to your site.  The nice thing about using one of the Google products is that you get to use the Google Domain Name Server to do the pointing.  See the Domain setup page for more about setting up a domain for Google Sites. Some of the same information applies for setting it up for Blogger but you can find more information by going to your blogger (or .blogspot.com) site and clicking on "publishing" under the Settings tab for your blogger site.