At the beginning I am new to server configuration issues. I have got a droplet on digitalocean VPS provider. Besides I bought domain on eurodns domain provider. Here I come to my question. Because of both sides have DNS Zone configuration I am confused where I should start configure that. VPS provider or domain provider? How do they interact each other? How about priority?
Thanks in advance.
You can choose to use either one of them (or neither - you could purchase DNS services from a third party, like Amazon's Route 53 product). Different providers may offer different features, reliability, etc. (to use Amazon as an example again, their Route 53 product has some built-in features useful for their load balancing, SSL certificate, CDN, and other offerings).
Whichever one you choose, you'll need to update (at your domain registrar) the nameservers to point at the nameservers provided by your chosen DNS provider. Once you've done that, set up the necessary DNS records there.
You can host your DNS with the company you purchased your DNS from, or point the name servers at your VPS provide and use their VPS.
In general I would avoid running a commodity service like DNS on my own server. There's nothing to gain doing that for most people, it's a little extra load and maintenance.
However, if the VPS provider provides dedicated DNS servers, that's an ok option. Then you would consider the features and reliability of the VPS provider DNS servers and your DNS registrar servers / service.
As @ceejayoz says, you can host DNS anywhere. I host my DNS on CloudFlare free plan. Super reliable, super fast. I've used Route53 in the past, which is good and costs
In general, for a beginner, I suggest you host your DNS on your domain registrar, because it's likely to be fast enough and reliable enough, but most importantly it's simple. Once you get everything working you can consider your VPS provider DNS, or better yet, CloudFlare / AWS Route53.
