Which is best apache web server or any web server to deploy my public folder.
There is no “best” answer here. Just depends on what your needs are.
Hugo generates static files that can be deployed to virtually any web server.
if your question is : “how can i setup up live my web site with minimum price and skills and maintenance problems”, you can look at www.netlify.com
If you’re really going to self-host, you can use nginx, apache or caddy.