What is the difference between the "Local Network" and "Local Network and VPN" options in Server
.local vs .private doesn't really matter, they're just different names.. the implications of .local vs .private just have to do with how DNS zones are created.  You'll be more interested in the security implications, because my belief is that LAN-only restricts services access to the local, private network; LAN + VPN opens it up to not just the local LAN but also the VPN connection/network (they're considered separate networks, remember,) and 'Internet' opens services up to the WAN.  If I were you I'd actually stick with LAN because as far as your server is concerned, once you're connected in to the LAN through OpenVPN, it doesn't care whether you're in the same room or not, nor can it tell.

LAN + VPN wouldn't screw you up but would set up Server.app with firewall and service rules allowing for the VPN service and its related networks to also access the services running on the server.

Hope that answers your question.