Moving To A New Server, Don't Wanna Lose Email

I'm migrating some accounts to a new server. So the dns will also change with it.

I want to ensure no email is lost in the process. Here's how I plan on tackling it, and I'm hoping you can offer suggestions:

1. Create all mail accounts on the new server.

2. Each person who has an account does the following in their respective desktop email applications:

a. Create a new mail account and use the IP of the new server instead of the domain name.
b. After a few days, update the IP to the domain name, and delete the old mail account.

Will this ensure no email is lost?

One other question:

What about the case where one of the sites has data updated each day? How to properly move this to a new server, without getting the database out of sync?