how many diaper covers do I need?

You should have a at least 4-6 in the current size range that baby is in. The qty. that you have depends a little on which ones you choose as well. Some of them are 100% polyester or synthetic, which means that if anything leaks onto them they wipe easily with a diaper wipe and dry so quickly you can use them over again with the next diaper. This means that you need fewer of them throughout the day.

If you use a more breathable diaper cover that is made primarily from cotton, you will likely need a few more covers on hand, since any leaks that may spill out onto the cover soak right in and can't be wiped off. Basically, you will need to toss the cover into the laundry more often and will need to have more on hand throughout the day.

Try out a few different kinds of covers the first round and then decide which ones you like best. Then get all of the kind that works best for you the next time baby makes a size change.