Renaming and subdirectory change at same time?

I have a WordPress site running with a temporary URL of //1.2.3.4/~myname/wp. I want it to change it now to run as //newdomain.com.

I thought I knew how to do this but managed to mess things up so badly that I had to restore to get back to a working state.

Should I change the site to //newdomain.com/wp first by pointing newdomain.com to my site, and then use “Use a pre-existing subdirectory install” second?

What cleanup steps might I need to perform after each step? I do have Velvet Blues Update URLs installed. Should I check all options? What about GUIDs?

Should I do those two steps in the other order? Or something else entirely?

Thanks!