Should I watch out for any pitfalls, beyond following the advice in the following useful post? For example, should I upgrade php/phpList on the old server before the transfer?
@Jonathan11 To reduce the number of differences between the old and new servers, updating to the latest release on the current server is a good idea. You can then do a clean install on the new server and copy the database and config file.
You will need to manually change various email addresses, URLs and domains on the Settings page to reflect the new subdomain.