I would do the migration as if I were moving the system to a new physical machine. Mainly you set up the new machine then copy over all necessary configurations, install necessary packages/programs, and copy data. Using rsync is a very handy way of copying the data since you can do the rsync repeatedly to get the updated data. Then you take a few minutes of downtime to make the final copy from an unchanging old server, swap IP addresses, and reboot both.