Selecting papers to read
If possible, find a survey, book, or a lecture note. This will help a lot to see the jungle through the trees! To find books, Google Books is your friend. Search the keywords in the Google Books, and try to find a relevant book on the subject.
Take the top-down / bottom-up approach, and alternate. That is, read the most recent papers first (the top research), and references thereof (bottom). Why? Because the top research is likely to be better, and has probably surveyed bottom works and improved them. However, to understand top, it is usually the case that you need to skim the bottom works. Important: Don't get stuck at the bottom. After reviewing older works, take the bottom-up approach. Finally, alternate between the top-down and bottom-up approaches.
Don't read a paper unless you are somehow sure that it is really relevant. The relevancy depends on several factors: The amount of citations, the fame of authors, the conference/journal it is published in, and so on. 
Be sure to read the title and abstract carefully, and skim the sections. Decide if you should ever read this paper now, and to what extent.
If a paper has a conference version and a journal (full) version, select the first one. The conference version usually gives the general idea, and avoids cumbersome proofs. Read the full version only when you really need to learn the proof details/technique.


Edit 1: Some of my colleagues use reference manager tools like Zotero to help them organize their references. I'm not acquainted with such tools, but I think you should give it a go.