Some regular readers know that I spend a week in Salt Lake City at the Family History Library every year. The one thing to avoid are the small pieces of paper for research notes.
Don’t take notes on small scaps of paper–they will get lost.
A research log is best, or some notes on a printout from the catalog listing the material that you are searching. If you must get a small notebook and keep notes. At least that way you’ve got your notes, unless you lose your notebook.