Hi Amanda,
Though ACR v9.3 has only been certified with Windows 10 and Windows Server 2012, I anticipate Windows Server 2016 to work just fine.
ACR v9.3 System Requirements
In regards to things to "watch for" while moving to v9.3, the upgrade process is consistent with the prior release. I advise the team to follow the upgrade guide's steps, as it will detail everything required to have a successful upgrade.
ACR/Summary and ACR/Detail Install Guide
Matthew Kennedy