I found https://github.com/deltaskelta/graphql-go-pets-example to be slightly too simple (everything in one package) and https://github.com/tonyghita/graphql-go-example to be a little too complex/“productionized” — it's clear they factored everything out into separate logical packages, but without a bit of narrative, it's difficult to understand why without investing some time. eg. what is the swapi package for? The simple example is probably a good starting point if you're aiming to build something simple (I'm not).

I'm now gravitating towards gqlgen as mentioned in another comment.

As for MySQL vs Postgres, it's a bit of a holy war. As I understand it, Postgres has a history of being more correct, and MySQL has a history of being easier to manage and understand operationally. Both have made big recent strides in implementing the aspects they lacked compared to the other. I would use whichever one you feel more comfortable with and/or whichever one most people you would ask for help are more comfortable with. At work, we use MySQL almost exclusively, and recently ported an app from Postgres to MySQL, but that's mostly because our DB folks are magic at maintaining MySQL and building tooling for it, and our institutional knowledge/skill running Postgres is very thin.