Newborn Diapering

So this has GOT to be my favorite part of cloth diapering, Tiny little bums wrapped in fluffy goodness :)

Q. How many of what diapers do I need to start?

A. It depends on how often you want to wash.

If you want to wash daily, I would recommend at least a dozen diapers a day. Multiply that number by the days you want to go between washings and that is how many you will need to start.  Keep in mind that your new little bundle is going to be up every 2-3 hours to eat, and for the first 4-6 weeks are going to be having bowel movements each time.  In newborn diapering you need to look at quantity over quality. Saying that, you don't want the cheapiest of the cheap on the bum, but you have to have a large enough supply to be successful!
When I started cloth diapering Madison, I started with about a dozen preemie prefolds and 2 or 3 bummis super brite covers.  I was washing daily.  I would wash her diapers with my sons one day, and the next day wash it with a load of her clothing, so hers were getting washed daily.  I had to rectify that quickly.
Prefolds are a staple in cloth diapering.  They are about the only item that will last from the first diaper change to the first oil change for the same child :)  I used mine for diapers, snotty nose wipes, burp rags, hot mats, doublers, liquid spills on the carpet and coffee tables, postpardom leak pads, etc...  You get it, there are one million and one uses for prefolds!  Most babies can go straight into infant sized prefolds, Madison was an exception at a mere 5 lbs 15 oz.  Abby was able to go straight to infant at 8 lbs 3 oz.  She also went straight into XS covers.
Next comes covers.  For the newborn stage, look for those with double gussets, and specifically made for newborns.  FYI, not many one sizes will fit all too well on a newborn.  Make sure to have at least 3-4 covers.  Most of the time you can simply wipe off any messes and re-use it, or let it air dry to rotate back in later in the day. You can look for covers with umbilical notches in them, and most XS or newborn will have this on there, but it is actually easier to have the diaper cover the umbilical area, as not all cords are at the same rise.  Don't weigh your cover selection on this alone.
For outings:
I don't recommended an ALL AIO stash for a newborn, as that would get quite expensive, and they don't fit the newborn diapers for too long, but I do suggest 2-3 AIO's for Dr visits, helping mother in law's, and daddy changes.  Most newborn AIO's run about $12-18 each, so it is easy to see why an entire stash of these could easily break the bank :)  Once that little Bean gets a little meat on their bones, you can start supplementing with pockets.  Some of the better fitting pockets I have found for my newborns are Rumparooz, Fuzzibunz and Bumgenius.  Rumparooz and Bumgenius take a larger slice of cake in my opinion since they offer aplix.  When you are dealing with a tiny newborn belly, sometimes snaps just can't get a secure enough fit.  Snaps however are GREAT later on!!
Wipes.  That HUGE stack of baby washcloths everybody gave you for your baby shower are going to be the best wipe for a newborn bum.  Thin enough to reach the tiny folds and sensitive skin, but soft and thirsty enough to get the mess cleaned up.  Moistened with a touch of plain water is all you need!
Many people are reluctant to start cloth diapering from day one for fear of meconium staining.  While it's nice to have bright white (or natural colored) prefolds, that meconium is some rough stuff, however, the sun is even more powerful, and free!  None of my prefolds, (even after 2 from day one diapering) have residual staining on them.  Don't let this fear keep you from starting early!
Some people will even opt for a diaper service for the fist couple months, to get them on their feet and into the cloth diapering routine, and past the itty bitty diaper phase.  Some retailers have caught onto this as well, and have started offering newborn diaper rental pacakges.  You can keep an entire stash of newborn AIO's and pockets for a couple months for minimal charge, and return it when you are done.
Finally, ENJOY the newborn phase!  It goes by so quickly!