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.