If I build a site on a test server, are there any special things I need to do when transferring to the final home?
Unless you have any hard-coded link in your templates/pages, you can just move around the whole folder and it should work fine.
Of course, setting up a new test instance (as a simple copy of the original one, but on a different URL) before deleting your old website is never not a bad idea.
Otherwise, you can just backup the files from Wordpress, just in case, to be sure.
Generally, you want to move the /user/ folder, nothing else. And even with that, make sure that the config files (system.yaml and site.yaml) is set up for use on a live server. Everything apart from the /user/ folder holds system files, no configuration or content, and it is better to not overwrite these files server-side.