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If it were me I would:
1. Transfer my existing site to the new server and get it working
2. Backup my existing website from the new server once working
3. Upgrade from 2.0.6 to 2.0.17
4. Make a backup
5. Update to the latest versions of my modules one by one, taking backups periodically along the way
6. Make a backup after steps 1 through 5 is complete
7. Backup again before updating to "2.0.17.1 Final" when it is released
But that's just me - others may advise differently