I created a zip file with the bare minimums and got it to launch in Local. Problem is that every link is a 404. The admin interface seems to be alright, and the front page loads with all the correct images/CSS/etc. But if I click on anything, it gives me a 404. On top of that, if I try to update a post or page, I get an error that says “Updating failed. The response is not a valid JSON response.”
EDIT: I solved this by going to the Permalinks section in Settings and simply clicking “Save” - which updated the permalink structure automatically.