
You are absolutely right when you say your fingers should not be touching the stamps.
The natural skin oils will, over time, transfer to the stamps and eventually cause damage.
The first item you need are a pair of stamp tongs. There are many types and if there is a stamp & coin store in your area, they would carry them. You can also order them on-line, but you don't get to hold them and see how they feel that way.
Good luck with your collection and welcome to the community!