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I have always used external DNS services because it is easy and reliable. Would like to learn more about DNS by trying to use my own.

I have selfhosted some apps on linux VPS and some more people have accounts to use the apps so it's not only internal. In domain registrar I have set name server to DNS service provided by VPS service. And in VPS console I have set the DNS records such as A record.

Not sure what I need to do and get started. Install authoritative name server (any recommendation?) on the VPS and set up same DNS records I set up with the VPS service? And change the name server with registrar to be my own VPS IP address? Seem too simple so could be I am missing some things.

Any problem with running name server on the same VPS as the apps?

Do you know some VPS services that offer decent DNS with API to add and change DNS entries? Unfortunately most I found myself have no DNS and the ones who do don't have HTTP API to use it.

For someone new to self hosting can you recommend cheap VPS to try simple things with? Can pay by hour like some cloud servers let you do or pay full month in advance.