Breastfeeding and Using a Bottle

This may be a stupid question, but I haven't found any information on this yet and I'm hoping some experienced moms may be able to help. I'm planning on breastfeeding and pumping for when baby goes to daycare. I've read that babys need different types of flow for the nipples on the bottle; newborn, medium, and fast. My pump comes with bottles but I can't find nipples that are compatible with it. Should I register for a different type of bottle so those nipples can be used? If I pump into the storage bags I should be able to use any type of bottle I want, correct??? Help!