I am currently writing a paper on 3x+1 and realized that despite having enough knowledge to work on a singular facet of the problem I lack a more broad understanding of the problem. I have seen the thorough annotated bibliographies by Jeffrey C. Lagarias but I do not have the time to read most of them and I imagine plenty of them would not teach me much about the problem itself, even if I did take the time to dissect them. So what are the papers people feel I should read with my limited time to gain the best possible understanding of the Collatz Conjecture?
It's challenging to distill a required reading on the Collatz conjecture, because it's unsolved. What may or may not be necessary? As you might have noticed from Lagarias's annotated bibliographies, there is a lot of literature on the subject, and it seems as though Lagarias has already sifted through a whole lot. What would be more convenient than his bibliographies, with short explanations of what each paper has done? If I were you, and I was set on working on the problem, I would decide which of the papers were related to the methods I had in mind, or which ones at least sound interesting.
I would also mention that the problem is unsolved, and so I recommend patience. Developing the patience to read a beautifully written set of annotated bibliographies might be a good place to start.