ZaleX

Usually, I used free service for DNS hosting, when I worked with digitalocean.com service I use their free option. But right now for my own projects, I use  Cloudns. I use the “PREMIUM DNS” plan, but there you can find a free plan too. 

In my practice (more than 10 years), I worked with many domain registration services. Like Name.com Godaddy.com and some others. But in my last choice is Namecheap.com. Price often more profitable than other providers (when you planing use your domain more than 1year). So you can try to use this service.