[ Since I read papers up and down up and down, and jump between sections, I wish there was a PDF reader that allowed me to split the screen like emacs, so i can scroll each independently.]
After that, save it as its full name, hopefully something grepable, but KEEP THE DOCUMENT OPEN. As you traverse the citation graphs, and slip your tentacles into the fatty folds of knowledge, try to mentally cross-reference the papers: see how they're related, the order of their publication, see if this is a lone paper or a family of texts emanating from a project. If it's a project or larger effort than a triplet of papers by 2-3 authors, then the project name will be your handle to this batch of texts.
Whatever your domain of specialization, you should have a mental model, however vague, of all the corner-stone papers, authors, era of publication, high-level summary of findings, etc.
You don't need to retain all the information in a paper. If you're a domain specialist, you're most likely interested in a finding or two in a few paragraphs. Feel free to pop texts off of your mental stack. You will always come back to them, most likely seeking a different piece of information (i.e. during the initial phases of your research you will be interested in the "what" and "how", but later your tastes will be refined and you will be seeking the "why")
Use a light-weight PDF reader, like SumatraPDF. You will have about 5 papers open any given day. The texts that interest you will most likely be "cohorts"; variations of a theme, perhaps some more introductory than others. etc.
This is how I read, and I don't recommend the 'wget -r' approach to researching.
In this case, since I've actually finished my degree, I just wanted to flick through a bunch of these on the train (without internet access) so it was useful to have an offline archive.
To do this I simply keep the same document open in multiple PDF readers at once (I use xpdf) and stack the windows either next to or behind each other, using a minimalistic tiling window manager (I use i3).
I did the same thing you're doing with Sumatra and Foxit, but usually I just take copious notes, specially to forward references. Then make a second pass at the document using my notes as guide.
