I was planning on posting this on academia.stackexchange, but I want an answer from mathematicians who've dealt with a similar issue when they were beginning graduate students. If this site doesn't seem to allow these sorts of questions, then I'll act accordingly to the comments.
If a student is beginning graduate school in a maths subject, then which research papers should the student begin reading? Of course, their primary concern should be their classes, the textbooks that they're reading, and the advice handed to them by their adviser, but is there usually a select few papers that beginning graduate students should read?
Of course, this depends on the subject, so, for sake of example, let's assume the subject is Set Theory. I would be reading Jech's text, but I would like to shower myself with the current and past workings of this field. Should I read say, Cantor's first published paper in this field? Should I just leave that as a lower priority than some of the more modern (and approachable) papers in this subject? Or should I just read whatever sounds interesting and develop strong familiarity with the environment of the subject first?
I ask because I've only read math textbooks, and I feel comfortable with them. I like reading the linear development of the subject, the theorems, definitions, and their proofs. However, at reading my first serious research paper, I feel very unproductive, unlike reading a maths text. It's probably because I have the desire to read through every claim that they make, and see if I can prove it, but it's usually very time consuming, and I feel like I'm not putting forth enough effort into reading for the forest, and instead only for the trees. This is why I wonder if there should be a collection of first papers I should read, so that I could get into the habit of consuming research level papers at a more productive rate.
Thanks for any advice.