If you are in an Active Directory environment, yes DNS switch is going to be your best bet. You can completely bring up the new host, copy all data, then have like an hour or so for a maintenance window. During that window you will make the database unavailable to end users, make one last sweep to copy any changed data then make the DNS change to point to the new host.
We had to do something similar for a program, the database was about 3.5 GB of data that we migrated over. Then created the new host, got a maintenance window, did a last pass through for the copy, made the dns switch and we were good.
That being said, we don't know your environment so i can't say for sure if this would work for your setup. Our database was being accessed simply by name, so we just changed the DNS record to reflect the new host. Our data was also flat - meaning it wasn't something complex like SQL, it was essentially just a file share with a ton of data.
