I also changed my host recently. My forum members were informed in advance of the change and when it was going to happen. I had my entire web site and forums ready to go on the new server by the big day. Since it is advisable to close your forum when performing a database backup I simply closed my forum on the old server for good when I began the process.
I FIRST changed my DNS settings.
Then I backed up my database and made a copy on a disk.
Then I set up my database on the new server and set up my forums using the same version of UBB Threads. After I verified that everything was working then I upgraded my version to the latest one at the time. This all took only a couple of hours and after another check on how everything was working I opened my new forums. (went very well with advice from the gents here I might add)
Once the DNS settings propagated users began showing up. I think I was able to access my new site and forums within hours and by the next day many of the regulars started showing up in the Who's On-line list.
To me, simply closing the forums was the least complicated option and since my members knew what was happening there wasn't one single complaint. When they started logging in they knew the move was completed and I knew that the DNS settings were pointing in the right direction.
I was and still am using Network solutions for my domain registrar... this post just reminded that they charge WAYYYYYY too much and I need to find a new registrar for my domains.
