If you are not going back to work anytime soon or ever, i would not feel the need to stockpile too much. when baby is first born, you have an oversupply and it will even out as the baby gets older (3-8 weeks). If you keep pumping, you will continue to have this oversupply, it is really up to you what to do.
as far as covers, i never used one. you could always use a blanket. i know a lot of women use udder covers.
kellymom.com :: Nipple shields