A mei tai baby carrier -- can be used in so many different positions and holds the baby very securely so that you don't at all feel the little one can fall, and works well into the toddler years.
A hand breast pump
swaddling blankets (and The Happiest Baby on the Block)
My husband says a good selection of bottles (BPA free)
vibrating bouncy seat
white noise machine
Good, large diaper bag (you'll be carrying stuff for both kids in it, no matter how old the older ones are -- we still often have stuff for our 8yo in there) -- we use a good backpack at this point with 3 kids)
A supply of infant tylenol, rash cream, teething tablets, etc. -- you want to have it if you need it.
If breastfeeding, The phone number of a good lactation consultant posted somewhere you can find it easily -- you don't want to have to start researching this in the middle of a nursing crisis.
Something I have my clients and students make (I'm a childbirth educator and birth doula) is a list of people and their phone numbers who they can call upon to bring over a meal, pick up some groceries, or come by and help out for an hour while you shower, nap or whatever, and a list of people and phone numbers who you feel you can call anytime of the day or night if you are having a crisis.
A freezer full of frozen meals that all you need to do is throw in the oven and dinner is taken care of. You've got plenty of time to make meals and freeze them so that they are what you normally eat. Okay, not really a baby product, but it sure does make those first few weeks easier.
That's all I've got off the top of my head, and I need to go get ready to take my 5yo to a birthday party.
-B.