This may be an obvious answer you've already discounted, but the solution that is at once the easiest and the most potentially customizable is hosting your own Wiki. This provides you with a simple edit/publish web UI like the GitHub document functions, and if your goal is to host or even allow collaborative editing of more self-contained formats (e.g. PDF), there are Wiki tool varieties with many different capabilities than the MediaWiki engine that runs Wikipedia.
If running on a VM, some stable/easy form of linux like Debian or even Ubuntu would allow installation of all the web hosting and database dependencies (e.g. Apache web server, LAMP stack), for which there are many guides.
Wikimatrix is a database of something like 140 wiki installations and tools, with smart comparisons based on features you need or your hosting platform. Might be too much information if you're looking for something simple, but very useful if you have something very particular in mind.
MediaWiki - familiar and powerful, fairly easy to install.
DocuWiki - Minimalist, based on text files so runs without database, simple in function and setup yet very capable. Allows the publishing of a series of documents very easily. Honestly, if you're basically looking for something to mimic the GitHub project readme or maybe the list of wiki help pages, this might be exactly what you want.
TiddlyWiki - very minimalist and lightweight, more for simple note-taking and editing (missing the more advanced Wiki features of DocuWiki).
TracWiki - software versioning and issue tracking features on top of wiki features.
Redmine - Software/issues with project management tools like gnatt charts, calendars, forums.
XWiki - A "second generation" wiki that, in addition to the basics of document editing and versioning/history, features inbuilt file management for publishing and potentially collaborative editing of PDF, office docs, and even movies. Also features collaborative tools like blogs, forums, and task organization and assignment. Steeper learning curve for setup, but very impressive as a single-software solution for hosting/editing many different types of documents.