I would say 6 to 10 covers is plenty. I don't change the covers everytime, only if they feel wet or are soiled. 6 would be enough for DS1 but I go through more with DS2 as his BF poos leak out of the flats more often.
Covers can be thrown in the wash with normal clothes so you can do them anytime, you don't have to wait till you have a full load of nappies. Actually I avoid putting mine in with the nappies, otherwise they are just covered in fluff.