Tom Denly (a well respected member of the hobby) identified 7 main areas of interest in a recent issue of Bank Note Reporter. I've [Bruce] split area 5 into 5a and 5b, because I consider them to be somewhat separate, and 7 into 7a and 7b because the world consists of more than just the USA. Alan Herbert added category 8. Steven Edelson added 9.
1) large-size US type notes
2) US national bank notes (issued by local banks chartered by the US)
3) US fractional currency (notes from the 1800s of less than 1 dollar)
4) pre-US colonial currency
5a) US obsolete notes (from private banks of the 1880s)
5b) Confederate States of America notes
6) small-size US type notes (the size we're familiar with now)
7a) recent and general world paper money
7b) older and rare world paper money
8) error notes, including printing, paper and cutting errors
9) Souvenir Cards
You can see the obvious slant toward US currency. Unfortunately, much of the really interesting US paper money is now very expensive. The very striking notes of the 1800s and early 1900s are now out of the price range of most casual collectors. Some people collect travelers' checks, and stocks and bonds, which might not be considered as paper money. Souvenir Cards (printed by people like ABNC) are a good way to see the beauty of currency.
There is a large group of people who collect world paper money. Some people focus on specific countries of interest and even specific time periods in specific countries. Often interest in paper money follows an interest in the general history as well. Some collectors focus on things ranging from notes with portaits of Queen Elizibeth to notes with pictures of boats to notes with specific serial numbers (all the same digit or very low serial numbers).
A very common type of world paper collection is to collect notes from "every country". The definition of every country can vary greatly, but this type of collection is relatively inexpensive.
One thing to keep in mind is that the quality of books on paper money is very high and they play a major role for collectors. Lots of people have dedicated their lives to researching and compiling information on paper money. It just makes sense to utilize and build on what they've already done.