domain name system - DNS/Web Hosting to a private network setup

I've tried to find a lot of answers to my question, but I am quite a bit confused to some of it and now I am here to seek further advice.

The setup:

We have a hosting and our domain will be something like this www.example.biz.

In our infra, we have the following traditional servers which will be put behind firewall and private network

1. Web Server


2. Database Server

Now the domain will be given to us and we would like to point it to our web server to host the web pages.

This was the solution I've come up,

Configure the hosting's domain to point the record to our Public IP which will be forwarded by the firewall through port forwarding to our web server and accept traffic to be able to serve this web pages.

My question would be, was my solution enough for this setup? or should I configure a public authoritative dns server and add it to the domain hosting's nameserver which i would still use my firewall to point it to my private network's web server.

I would really appreciate for any advice there is, I am still new and I've found this site very helpful.

Thank you and Regards,
Ian

Answer

You don't need to run your own DNS server. DNS is a basic service, you can rely on your provider or a third party like CloudFlare / AWS Route 53 for that.

Other than the DNS part of your question your solution is standard and should work.

A note: firewalls don't exactly "forward" traffic, I would say they intercept or pass through traffic but that's mostly a semantic difference. A reverse proxy server like Nginx would forward traffic.