I can only tell you what has worked for both my kids. Yours will inevitably be different, but…
A bouncinette. I was given a crib, a co-sleeper, a bouncy seat and a swing for my kids to sleep in during their first days. I tried each one and none of them worked. But the bouncinette was home to my first for his first four months and the second (who is 10 weeks old Friday) since the first week. She’s so freaking tall, though, that her feet have already reached the end.
I also love the First Years Deluxe Fold & Go Diaper Kit. I use it in place of a diaper bag and, if I happen to need a bottle for expressed breast milk, I just toss the bottle in my purse. I have a large purse, so the Diaper Kit fits, too. I can fit extra wipes, a bag for old diapers, two extra diapers and a change of clothing in that thing, plus I don’t need an extra bag.
I strongly recommend a sling or baby carrier, too, though definitely try it on first. I have three and use one. Thankfully two of the three were gifts and the one I bought was not expensive. The one I use the most is a regular cloth sling, then the Baby Bjorn (which my daughter hates, but is more comfortable) and I’ve never used the Boppy sling I have. I used the cloth sling until my son was 18 months - it was a great replacement for a stroller while we were traveling in India.
When you get to high chairs and solids, or even before, if family meals are important to you, I strongly recommend a Space Saver high chair. That way they won’t be separate from the table and you don’t have to skirt a separate high chair. We have a pub-height table, so we also didn’t have to lean down to feed our son. Although our daughter has yet to start solids, she already sits at the dinner table with us in the evening (we rolled up two blankets and put one on either side of her head for support).
Things I’m glad I have but would consider optional include a changing table (you can stock it with everything), a running stroller (very smooth ride and I work out a lot, but you can’t use it until your baby can support his or her head well) and a baby bathtub (makes baths much less awkward). We rarely used our travel system stroller or umbrella stroller, but the travel system is useful when they’re really little. As soon as our son learned to walk, we had him do that and kept the sling in my purse and just popped him in that when he got tired.
I kind of wish I hadn’t gotten a diaper champ. We had a tendency to get very lazy about putting out the diaper trash, so we just use plastic grocery bags now and take them to the trash every morning. Our house doesn’t smell at all now (it helps that she’s breastfed exclusively, too - formula poops are much smellier, at least in my experience), though when we had the diaper champ it smelled like shit. Literally. But your mileage may vary, of course. If you’re not lazy like we are, it probably won’t make a difference.
Other than that, I would strongly recommend if you’re breastfeeding to learn the side-lying nursing position. Definitely master the other holds, but side-lying allows you to lay down while feeding your baby in the middle of the night. Your lactation consultant should be able to help you with that.
Also, keep an eye on your posture when you’re nursing and do core exercises if you can. Women have a tendency to hunch their shoulders when they breastfeed (unless they’re laying down), so that, combined with walking and carrying your baby, can do a number on your back.
I would wait to get a breast pump (if you need one sooner rather than later, they’ll let you use one at the hospital and will let you know on your way out where you can rent one) and most of the other big-ticket items until you start needing them, as suggested earlier. Also, I’d wait to get toys and, when you do, try them out on your baby at the store before you buy. I got my little girl a few toys and she cries whenever I show them to her. Some kids just don’t like 'em, I guess.
Another thing (or things) I’d wait to buy include stuff like special outfits. My son and daughter lived (or still live) in onesies and footed pajamas the first months of their lives. I was big on them wearing something they could sleep in at any time.