What iCloud backs up > iCloud: Backup and restore overview
Other files can be transferred using the Migration Asssitant > Mac mini Fast Start: The new user's guide to the Mac
The other option is to boot the old mini into Target Disk
mode and then connect it to the new Mini with a Firewire800
cable. Then use Migation Assistant to transfer. This will
actually be somewhat faster that the ethernet approach as
there is no network overhead in the data transfers and is
straight disk to disk data transfer.
If you want to spend the money for a Thunderbolt cable, this
transfer will be lightning fast. Basically as fast as a SATA
hard drive can transfer data.
For using Target Disk mode see this: