Perhaps using MediaWiki's page import/export functionality will work for you?
https://www.mediawiki.org/wiki/Help:Import https://www.mediawiki.org/wiki/Help:Export
It's cleaner than storing the whole database in Git, and the XML import/export files are mostly human-readable. They can only contain pages, so this will take care of categories and the templates, but it won't handle e.g. defining an administrator account. Also, note that there's no easy way to "undo" an import (you'd have to delete or revert the imported pages by hand).