There are only a couple of options that are viable for today's collector.
Sleeves versus Sheets --- You are going to want to store your collection in a manner that also allows for display when you want to show it off. This basically leaves plastic holders that allow you to see both sides of the banknote while keeping it completely protected.
These plastic holders come in a variety of types. One of the most popular fits into a 3-ring binder or fits into a special binder designed for currency (the special binders can be quite expensive.) The binder sheets come in a few sleeve configurations: one big sleeve, two sleeves, three sleeves, four sleeves or even six sleeves (designed for baseball cards but works well for small currency like notgelds.)
There are also plastic envelopes or loose single sleeves (of various sizes) which are sealed only along the bottom edge or sealed along the bottom and two sides to allow access to the sleeve through the top. These sleeves and the enclosed banknotes can be easily accessed when stored in drawers or boxes by country name.
PVC versus Mylar --- Once you decide whether you want to use binder storage or a drawer type storage system containing sleeves you are ready to move onto the MOST IMPORTANT issue: what type of plastic holders do you use?
This is most important because if you choose wrong the plastic you thought was protecting it can destroy your whole collection. The off gassing from plastics containing PVC (Polyvinyl Chloride) is extremely harmful to paper products (I've heard one of the by products of PVC off-gassing when combined with humidity from the atmosphere is hydrochloric acid). After some number of years (I've heard anywhere from 20 to 50 years) of storage in a plastic product containing PVC, paper products dry out completely making them brittle to the touch. After an extreme number of years, your banknotes may disintegrate in your hands when you eventually try to remove them from their sleeves. The PVC can also cause a brown discoloration after a number of years as well.
You want to make sure you only buy and use MYLAR EQUIVALENT plastic products to store your banknotes (and all paper collectibles for that matter). Mylar is a brand name for a plastic product that is archival safe. There are equivalent products on the market as well that may be a little less expensive.
Other Considerations --- Naturally you also want to store your binders or drawers in a location that is safe from liquid damage, child damage and even fire damage if possible.
Also, whenever you are showing off your collection, be sure to instruct people viewing it as to proper handling to avoid damage due to ignorance. Many people just don't know how fragile and special the banknotes are. People often want to take them out of their protective sleeves but that is just asking for trouble. At the very least they'll get oils from their hands on the paper which can discolor it after too much handling.
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 portraits of Queen Elizabeth 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.
RESOURCES:
WWW.COLLECTORNETWORK.COM
WWW.COLLECTPAPERMONEY.COM
WWW.WSCOIN.COM
WWW.FAQS.ORG