When it comes to customizing Discourse, you have several general options, ordered here from least to most painful and dangerous:
Level 0: “I want to change what it says”: Adjust your admin settings
Visit /admin/customize and edit ‘Text Content’ or ‘Email Templates’, which will allow you to replace any string in Discourse or its currently installed plugins
Level 1: “I want to change how it looks”: Write (or install) a theme component
Visit admin/customize/themes and download or write your own CSS and javascript to be applied to your instance. This will (generally) only affect the look and feel of your site, rather than changing any substantial functionality (although you could change functionality pretty significantly too on the frontend with these 
) Extensive guides for installing and writing themes are available.
Level 2: “I want to change how it works”: Write (or install) a plugin
If your changes need to affect not just how your instance looks, but how it behaves, (including but not limited to what information it stores in the database, how the server processes information, or what restrictions exist around viewing, saving, or manipulating information), then you need a plugin. Extensive guides for installing and writing plugins are available.
^^ (NB, you are solidly in this category of functionality here, iff you really can’t find any settings which meet your use case, which I still think you may be able to)
Level 3: “I want to make a new product based on Discourse”: Fork the repo
This would generally be reserved for a person or organization who wants to take the Discourse codebase, customize it very heavily, presumably for the purposes of reselling it (which is allowed under the copyleft license).
Even in this use case, I’d probably opt for building a suite of plugins (I believe like what @angus is up to), so that I could more easily take advantage of the new security fixes, performance enhancements, and features that the Discourse team will be working on. That’s to say, there’s not a lot out there that can’t be accomplished with the first three options.