Best way to start a new blog?

I think you may download the latest version of wordpress program. After that, install your purchased theme to the system. You can go to Appearance > Install Themes > Upload to install your new theme. You can just find any hosting which supports php becuase wordpress is written by php. godaddy is one of the options.

Scott,

here is what you need to do:
- register your domain with a decent registrar (my choice is namecheap.com; I'd advice anybody against using GD for anything - especially not for hosting!)
- get a cheap hosting account with a decent hosting company: you can get from $4-5/mo

The hosting company will give you the NameServer information (DNS). Usually, it is 2 lines of code, like ns1.example.com and ns2.example.com

Take those 2 lines and at your registrar enter them where they ask for DNS info.

In plain English: after registering the domain(s) you point them to your host server, so anybody clicking and/or typing your domain address will be directed to the place (your host's server) where your site is going to live.

Then install WP in the root directory (usually: public_html) of your server:
Installing WordPress « WordPress Codex
(on that page you can find everything you need to know, just read ALL of it )

When you buy or download a new theme - those are, usually, in zip (compressed format).
Unzip it and you will get a folder (directory) with a lot of files.

Using your FTP upload the whole directory into /wp-content/themes/ directory.
more reading: Using Themes « WordPress Codex

Log in and activate your new theme.