4 is the correct answer This is a bare minimum for variety. I typically have between 10 - 12 but find with that many, I don't play some of them as often as I should. However, I think a very comfortable number is 8 because as anyone in this hobby knows - there is always something breaking so you can assume you will always have something unplayable.
Seriously though, you will have to collect for a while until you determine the right number for you.