I'm going to attempt to move to a new server sometime between now and Tuesday. The general progression is something like:
1) Forums are frozen.
2) DNS is updated (and how long it takes to update depends on where you are in the world).
3) You're on the new server!
You'll know when it's happening if you try to visit TLHH and see a maintenance message. On the other hand, you may miss it entirely.
I would recommend not touching the wiki until we're done moving and not uploading any attachments to the forums.
GEMP players should be fine either way as images should load from whichever server they get.
GCCG players will be fine until DNS updates to the new server, after which they'll be unable to connect.