My goal is to have a REST endpoint that I can push AJAX requests to, have those requests be parsed, potentially push some data into the DB via a channel, and then return a JSON status message. I don't want to have to put PHP into a template to accomplish this, and am happy to write an add-on of some sort.
Please don't suggest add-ons. I want to know how I would go about writing my own add-on to accomplish this.
From a high level, how would I start writing this add-on? Specifically, how would I route a custom URL to my add-on code? What type of add-on should I be building for this (i.e. Module, Extension, something else)?
This is something I've done a number of times with other web frameworks (including CodeIgniter), but for some reason I'm finding it very difficult to get information on how this would be done in EE.
EDIT: I've tried to make this question more clear. I'm specifically looking for advice about add-on creation. Based on my re-reading of all the EllisLab add-on docs and a lot of time searching the web, I'm starting to feel like this isn't something EE can do without an incredible amount of hacking. I'm really hoping that's not the case.