I can personally recommend
Stable Host (VPS),
Blue Host (Business Hosting), or
Interserver.net as I have used, or have worked with clients who have used these providers.
I do not know if they offer migration services, but
it is something that I offer if they do not.
You do not have to migrate your site from within UBB.threads, in fact I would advise against using any backups created from the admin script as they will be subject to the PHP max execution time setting, which could leave you assuming that you have a solid archive when you in fact only have a chunk that was created up until the connection timed out.
A backup should be created (and restored from on the new machine) from the command line interface (SSH), as discussed in my
Migration Guide on
UBBWiki.
