Well that was a no brainer!
My host uses C-Panel which has Fantastico installed.
One of the options is install Wordpress! AND it's the current version.
One click and it was in. It only asked me what (sub)directory I wanted to install to, password and user name.
Had one potential problem. I thought I would install to an add-on domain on my account. This looks like a sub domain in some ways (creates a subdirectory of the html_public directory called the add-on domain name) which I thought may confuse the installation, but no problems. Fantastico offered the installation to either the main domain or the add-on. All URIs resolve to the add-on domain name. SIMPLE
Once "inside" , I changed some of the defaults and activated some of the included plug-ins. Inserted the notification email address, tagline and title. Set it for pretty permalinks. I also added the list of common spam words from Wordpress.
Now to try Movable Type.