While migration, you should first transfer the data files, and databases on the new server, check all the settings on the new server once the migration completes, also check the websites through temporary url or if you have plesk then through plesk site preview.
Once you are confirmed that everything works well on the new server, then you can resync the data as soon as it completes you can update the name servers.
By this you can achieve minimum downtime , i.e downtime will only for DNS propagation which
AFAIK , usually completed in couple of hours
