Embarking on a Voyage of Scientific Discovery

how many of each class of notes does one need in order to make it worth going back to fallen London?

how many Pages of Cryptopaleontological Notes?
how many Pages of Prelapsarian Archaeological Notes?
how many Pages of Theosophistical Notes?

also, is there a real benefit to playing the "Share your Research with a Fellow Scholar" card?
I don’t have any friends eligible.

The game treats each page as if it were worth 10 pence. But it really depends on what you intend to do with the notes. If you just want to turn them into money, the 500 page options in your lodgings are much more valuable than turning them into Collated Research, though this leads me to believe the souvenir volumes of your work may become useful in the future.

Sharing the research doesn’t get you that much, and you actually lose your ten bats in the process. The best thing to do with it is hold it in your hand so you don’t draw it again.

If you’re Unwelcome at the University, you’ll need 500 pages of all three types to rectify that situation. If you’re a monster-breeder, 500 Cryptopalentological Notes are required for the last step there. If you don’t yet have a Voluminous Library, you can get one for 250 pages of all three types, which is I believe a better deal than the Legal Documents.