Postgres is a better option to consider compared to MySQL. With respect to performance, postgres has an edge over MySQL.
Don't use net/http for production. Read this https://medium.com/@nate510/don-t-use-go-s-default-http-client-4804cb19f779
I prefer gorilla/mux as it is simple and provides all the basic features.
Other lib seems to be an overhead if you just need basic routing.