Before you finally cut ties with your OLD host, practice what I say above.

If you make errors, you can always delete the database on the NEW server, and try all over again.

Generally, when I move hosts, I don't "wave goodbye" to the old host until I see my stores operational on the new host. I also have a dedicated "dev" server where I move all my clients to anyway, so I ALWAYS have a "working copy" of all websites - just in case...