Why do you need your host to handle the DNS?
You can just set the DNS records directly at your DNS registrar (like at NameSilo, NameCheap, etc).
For the root domain and the "www", point the A record to the server IP. You'll probably also want to set an MX record, and maybe an SPF record.
Find out from your host if there's anything else you need to set. (For instance A records for a mail. or ftp. subdomain.)
(One thing that you still might need to set at your host, is a reverse DNS. They'll probably do that. It's not that crucial to my understanding though.
Some info about it here:
What is "reverse DNS" and do I need it? - Simple DNS Plus )