Hi,
Your server is currently without any protection if your windows firewall is turn off.
Question : If so do I install a Managed client, Unmanaged client, etc.?
Ans : Install it as a Managed client
Question : If it is managed do i use the network share or do I Push the client?
Ans : Manually run setup.exe on server by selecting required features (AV /AS, PTP / NTP).
PTP is not supported on server operating systems even you installed it will remain in OFF mode.