A good carseat that you are very comfortable using and installs well in your car.
Sling(s) that work well for you and baby. I prefer pouches for tiny ones, and Mei Tais or SSCs for later. I've tried wraps and ring slings and neither worked well for me.
Prefolds (ie burp clothes), wipes, diapers and covers, large wet bag(s) for the pail, smaller wet bags for the diaper bag
Comfy easy baby clothes - sleepers, gowns, onsies, t-shirts, etc
Nursing pads (I leak too much for cloth
) and good nursing bras
A bouncy seat for the bathroom for while mommy is showering or using the toilet
A bag for when out of the house
Something to protect the sheets and mattress from leaky baby and mommy messes. I used prefolds and receiving blankets for DD1, and a nice wool blanket for DD2.
A camera 
As baby gets older:
a high chair, bibs, baby/child sized silverware, dishes that can be thrown on the floor, and cups
an exersaucer or other baby containment device for in the bathroom (my older babies/toddlers always got into all sorts of trouble in the bathroom while I was using the toilet or showering if allowed to roam)
Oh, and toiletries:
shampoo/soap/diaper cream
nail clippers
brush/comb
thermometer
basic selection of medication you're comfortable with giving (Hyland's teething tablets, infant Motrin, we use Tiger Balm as a chest rub for congested babies/kids, etc)
lanolin or other nipple cream
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