Although fonts are not neccesarily bought as collections – more often they are bought one font or family at a time – but you could start here:

http://typophile.com/node/30047

There are no such things as must have fonts though, it all depends on what you do with them, what you like, and what’s your budget. You could do searches on Typophile for threads on what people consider the best or essential typefaces. What you will see though is that these lists are different from person to person.

If you are a student, there are some additional options available to you for inexpensive font collections.

Regarding books, currently I suggest the following as the optimal $100 type designer’s starting library:

Fontographer: Type by Design by Stephen Moyes (out of print, used)
The Stroke by Gerrit Noordzij
The Elements of Typographic Style (4th edition) by Robert Bringhurst
Designing Type by Karen Cheng
Anatomy of a Typeface by Alexander Lawson

Notes:

I would have Letters of Credit by Walter Tracy on the list, but it is not only out of print, but horribly expensive.

The Fontographer book may seem very software-specific, but it is actually a great general intro to how to work with bezier curves and the like.

Karen Cheng’s book is a bit polarizing for some folks, but most of us seem to think it is useful. Yes, you can do most of the same analysis on your own with a decent library of fonts and a font editing program, but it would take a bunch of work; somebody else doing that for you is helpful, IMO.

Finally, other books may come into play depending on what font editing tool you use. The software manual itself may be of use....