I would suggest you start with analytics and testing. This way you can test everything and use GA (or whatever) to gain insight into your app/sites usage.

If you wanna really geek out, try to learn HTML+CSS and build some mocks.

Logs? After you review a prod log and notice a bug or exception, you create a bug and assign it to a developer. I guess this could be helpful. But that dev will probably review the same log and do some tests to find a root cause then go fix it. I feel the same for any log review or server/app alerts. Unless you know the code, its simply one interpretation.

Editors? I'm not sure this will help out much.

Git? I think that anything git related will eventually lead you to code.

Testing + Analytics, imo, should be your sweet spot for now.

Good luck.