Are these DNS settings a good idea or not?

Solution 1:

Workstations should have your internal DNS server(s) as the only DNS server(s) in TCP/IP configuration

PCs pick DNS server from the list and stick to it for some time. So if by some chance your workstations would pick your modem or Google DNS server, your internal AD domain name resolution would stop working.

You can optionally have Google or modem's DNS servers specified as forwarders on your DC's DNS Server. But DNS server on DC could also do all external resolution without any forwarders. Using your ISP's DNS servers as forwarders on internal DNS server might make more sense though. But you don't need to use any forwarders at all