This is what I do:
Buy a domain
Set the DNS to whatever host I plan to use it on
Log into my control panel for that host
Setup the domain
One-click install wordpress
Log in to wordpress, install the WPMUDEV dashboard plugin (WPMUDEV is not free, but its really nice)
Once the wpmudev dashboard is installed, I can one-click install any of the plugins or themes that they offer right from the dashboard
Then I install a couple of other plugins that I keep in a folder, just for setting up new wp sites
I can go from domain purchase to operating website in about 10 minutes, with facebook and twitter integration.
Of course, the first time took quite a while longer. But soon I got it down as a system and now its really just a few minutes to set up a new site.