I started reading back in early 2000 and it took me two or three weeks THEN to read through everything. Now granted, there were a lot more active authors still then, and so I read everything. But yeah, you've got a bit of a task ahead of you.
Having said that, I would say that after you read the Core, read TWILIGHT, and then start into the Future Imperfect era, and go back and fill in occasionally as needed. There are some real gems in the earlier stories, but if you don't get the older references, you can probably skip them. YMMV, though.