There is no solution to “boot iPad straight into an app” like macOS or Windows.
But, after booting to home screen, guided access, some third party remote control solutions, MDM, you pick. Awesome suggestions listed above to lock down iPad into single app mode.
One grip however is there is no MDM profile that can disable auto update. The best bet is to download tvOS profile to stop auto update. Any latest one would work.
As for the backup, just setup wifi backup to iTunes.
PS: guided access also disables the home bar on iPad Pro and iPhone X/XS.