Netlify seems pretty great. Use whatever site generator you want, and Netlify will handle the continuous deployment from a git repository. They can add even more value by doing things like automatically giving you HTTPS. However, you can’t use their automated service if you manage your own DNS.
Here follows a summary of what I had to do to get LetsEncrypt going with Netlify (aside from the stuff I had to do to get Netlify working with my repo and Hugo in the first place).