Newborns use more covers and diapers per day than any other age.
Most newborns use 10-12 diapers each day. If you are using prefold diapers 6-8 covers each day are recommended. For fitted diapers, 4-6 covers each day are recommended. The newborn Prorap Classic and the newborn Bummis Super are both good to use with prefolds. If you want to use a fitted diaper (like Kissaluvs for your newborn I recommend the Bummis Pant as your cover.
If you want to use prefolds you can use the newborn (infant) 4x8x4 diapers or the regular 4x6x4 diapers. The newborn diapers will give a slightly trimmer look. The 4x6x4 will look big at first, but you should be able to use them until potty training.
The only All in One that I have found to work well on a newborn is the Proservices All in One diaper. The Proservices AIO diapers have an extra leg gusset that the other AIO don't. It helps keep bf poop from leaking. They also have a notch for the umbilical cord.
Some people find disposable liners like the Biosoft and Imse Vimse flushables to be helpful although they are more of a personal preference than a necessity.
You shouldn't need any extra absorbency at this point.
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Jeanne's Cheapest Route for the first year:
Use prorap classics - 8 newborn, 6 small, 6 medium
Use regular prefolds - 2 to three dozen
Diaper Pail
(reduced cost shipping if ordered all at once + taxes if applicable). You will be washing every other day with this set up, but you really don't need anything else.