There are so many things I could list as stuff that make early child rearing easier. It's hard to winnow a list down to the bare essentials and so much of what we love is ineffable. Also, some of the biggest essentials we have found are things like affordable child care and good friends.
But, if a new mom asked me, though, this is what I'd tell her she wants:
1. Bottle rack (ours is from Munchkin and we love it) plus a bottle brush. We wash bottles at least a gabrillion times a day. It helps keep the clutter not so cluttery. And you don't need a fancy pretty one that costs a lot. the Munchkin one we bought at Target. It folds. We've traveled with it. LOVE IT.
2. Digital Camera. Seriously? If you don't have one, you need one because you turn around and suddenly Junior has a pack of cigs rolled in his shirt sleeve. Record everything. It's all deletable.
3. If you do have a digital camera, upload to Flickr and get a pro account. With a pro account you can sort things into albums and collections. And you can print to a nearby target. It's fabulous.
4. Bulb aspirator is a must have. Babies hate the snot sucker, but they totally work. Our hospital sent us home with one.... and hospital grade snot suckers are perfect.
5. An Ergo carrier. It's the most comfortable of carriers we have tried (and we currently have a Bjorn, Two Sherpanis and two slings). You can wear the baby on front or back, both are extremely comfortable.
6. A foam tub insert. The actual baby bath set isn't necessary, but a foam insert lets the baby float and kick. Little Man adores bath time.
7. Hand sanitizer. We keep ours at the changing table and where we keep bottles.
8. BTW, speaking of changing tables: we don't use ours except to store stuff like unfolded laundry. We do use our Graco Play Pen for changing, storing, and for nap time. In hindsight, I might have foregone a crib and changing table and just gotten this!
9. Other good thing to have: an address to a local consignment store. New clothes for babies are fun to buy, but it adds up. Consignment is totally the way to go since babies generally outgrow before they wear something out. In LA, we have a several from which to choose plus a twice-a-year giant consignment sale. Sometimes it does pay to be a huge metropolis.
10. (Fine. This one isn't an essential, but it sure felt like it at the time). If you are going to use cloth diapers (go cloth! choose cloth!) an essential, at least to start, is a diaper service. We had ours for 3 months and it allowed us to get used to our son and everything. else without the stress of cloth diapers. It let us get to know a little about parenthood before we had to invest tons of $$ into diapers without being sure we could do it.