A chair- A.K.A. somewhere to put the baby. We have the FP Infant to Toddler Rocker and it has been a life-saver. The nice thing is that we could use it pretty much right away, and it was invaluable as a "put the baby close to me while I shower" chair in the early days. Now that he's bigger, the kiddo has figured out how to make himself rock and it's awesome.
A carrier- because unless you have a full-time maid, sometimes you need 2 hands to get stuff done around the house. Up to 3/4 months we used the Moby, which I LOVED. It keeps the baby nice and close; he slept while I did stuff, and it was a lot nicer than the stroller when he was a tiny little thing. Now we use the ERGObaby carrier, which I also love. The most important feature is the hip belt that takes the weight off your shoulders. (For reference we do have a Bjorn type carrier with no hip belt and I could only use comfortably it for very short periods of time).
Stroller- because you won't always want to carry the baby on you. Good for walks- from around 2 months the kid became very interested in trees/nature, and so he has his own seat at restaurants before he can sit up (personally I'm not a fan of carseat on the chair/table contraption). We use ours - the Baby Jogger City Mini- every day! Decide what features are important and go from there. In our case I need big wheels for the crazy Mexican side walks, a big sun canopy for the Mexican sun, and relatively light-weight stroller because pushing a baby up a hill is work enough.
Car seat- Check the ratings and choose one you like. Install before Baby comes home from the hospital. We have the The First Years True Fit C670 Premier Convertible Car Seat and have been happy with it. If you are going to be driving a lot, I would suggest an infant car seat that can be removed. Even though it is very heavy to carry around, sometimes it can be useful to take out Baby + seat.
Fabric- burp cloths, wash cloths, blankets. You're going to be wiping lots of drool, spit-up etc, plus Baby is going to go on the floor a lot, and you want to be able to layer to keep Baby warm easily. So you want lots of these. We have about 15, 12, and 8, respectively, plus the 8 swaddle blankets I already mentioned, which can also be used as burp rags/nursing covers/blankets. I think you can probably do with a little less, maybe 12, 8 and 6, and still not have to do lots of laundry but as you know variety is the spice of life.
Playmat- We have two: the Baby Einstein Neptune Ocean Adventure play gym, and the FP Discover 'N' Grow Kick & Play Piano Gym. Our kid loves the latter- the piano is awesome. I would say from about 2 months on, this has been a life-saver in that I can leave him playing for a few minutes and he is totally entertained! Also, foam pads if you have tile floors like we do. Playing on the floor is a must for letting Baby explore.
Books- Mostly for your own sanity, I would get several. We read every day and the older he gets the more Baby Boy enjoys the books. Even though you can technically read a baby "anything" just so that pick up on words, sentence structure and language fundamentals, children's books with colorful drawings seem to keep his attention best.
Toys- there are a lot of options out there, choose what you like. Our one stand out toy that Baby Boy really loved from about 6 weeks on and is still totally enthralled with is the Lamaze Jacques the Peacock.
Monitor- I would throw this in as an optional item. I use ours very infrequently since our house is not that big, but I will set it up for nap time if I need to be on a different floor and there's noise to the point I might not hear the kid.
That concludes my series of STUFF. The rest of the posts can be found here: