Docear (
http://www.docear.org/) + Zotero (
https://www.zotero.org/), with Emacs+AucTeX for the writing.
They all fit together.
>- recording notes and ideas from papers
Docear's core is a mind-mapping application that is used for taking and linking to different notes - you can take notes using whatever app you want and then add it to the mind map-
> - recording where I got a paper from, ie was it referenced from another paper or found on a particular site?
With Zotero this can be as simple as a click, it adds the current page and document along with metadata and can export it to bibtex or the like, thus tying it to docear.
> - even how to read a paper.
This is not a technology problem, investigate approaches such as SQ3R (https://en.wikipedia.org/wiki/SQ3R) which is the one I use (actually the variation SQW3R) or PQRST (https://en.wikipedia.org/wiki/Study_skills#Reading_and_liste...). I keep a low-tech approach on purpose for this, but there is nothing preventing using Docear for this as well of course.
>Right now I use google docs with sub folders for unread, read and implemented papers. I tend to use Acrobat to highlight sections of a paper that I find important and Evernote for saving more important notes.
Docear is supposed to be used with PDF annotators, it then scans the PDFs and automatically creates the references mind map.
> If anyone has a good system for how to read papers more efficiently, how to store notes/annotations for a given paper, or how to track a todo reading list I'd be very appreciative!
For reading them take a look at those I mentioned before, SQ3R has been useful for me in terms of articles and books. To store things Zotero is very good for anything which is done via browser. Docear is useful for managing different "projects" (could be disciplines, specific papers, etc). For TODOs you can either also keep them in Docear (since it has a mind mapper you can create a new node and add the references you exported from Zotero there, actually Docear scans the library and automatically adds any PDF to a specific node) or use something like Evernote.