You need at least two nodes that do DNS, DHCP, NTP, and other miscellaneous services that you absolutely want to have but do not seem to have mentioned. You want them to be permanently assigned, so that you never have to search for them, and you want them to fail over each service as needed, preferably both operating at once. Three nodes would be better. Consider doing some basic monitoring on these nodes, too, as a backup to your main monitoring system.
1&2. Authoritative DNS (internal)
1&2. NTP
1&2. Caching DNS resolver
3&4. Outbound HTTP proxy (if necessary)
3&4. PXE / installer / dhcp
3&4. Local software mirror (apt / yum / etc.)
5&6. SSH jump hosts.
Or something like that.
Make sure the second host is not just in a separate chassis from the first host, but also in a separate rack.
For external authoritative DNS, don't do it yourself -- pay for someone to run that for you (Route53, ns1, etc.). For e-mail, if you can possibly not deal with it then don't -- use Mailchimp or something.
The DNS records for the internal records are done using the kubernetes middleware (basically serving the service records). The external records are pulled in from a git repository hosting our zones as bind files. If need be zones are split into subzones per team/project. Same permission system as our code via MRs using Gitlab.
Our recommendation is build on open standards (BIND, AXFR) and use services on top of these.
I agree that using an external mail provider is usually a good idea. It mostly is your fallback communication channel and is usually easy to switch (doing replication to an offsite mail storage needs to be done to make switching easy/possible/fast). MX records \o/