Hi Doug, it is not a big deal, there is a lot of advice on how to migrate your Moodle, and having run afoul of some very simple processes once or twice, it is not much fun. Not having done a full site restore for a long time, I am not allowed near servers these days...mmm..., it is likely all different now, and I do not seem to be able to find any Moodle Docs on creating whole course flat files. The database is easy, but the real risk is the moodledata folder.
Download and install a test site, then run backups from your production site, restoring them into your test site, see what is restored. It should all be there, everything, BUT... all paths in the mbz files are relative, which means that all restores are set to use the path in the config.php file, so make sure that is happening. Just do a couple of courses to test things out.
From there, it should be fairly straightforward.
Of course, you could just migrate your Moodle to the new server, then upgrade the codebase, rather than restore into a newer version, vanilla Moodle. This allows you to test things before upgrading and, once upgraded and tested, you can make the new site live without any disruption to your clientele.