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Make sure you have some newborn diapers & clothes. If you don't have any, you also need wipes. You won't be bathing the baby until the umbilical cord falls off, so that's not an absolute necessity at this time. I like to be prepared so I bought everything I could have possibly needed. It was overkill... Also you need to get all your nursing stuff ready to go (obviously). I sent my DH to Target for the gel nursing pads on many occasions.

I would get one pack of newborn diapers since you never know how big the baby will be. Then some size 1 to have ob hand too. cause one day the newborn will be too tight and you don't have to run right out. You can not have too many wipes. We have a basket next to the changing pad with hand sanitizer, diaper cream, lotion(for after bath), Boogie wipes, and some other face wipes. The hamper is on one side and the diaper trash can on the other.

I would have:

+Coffee/coffee machine and mugs easily accessible near(ish) your bedroom - for DH!
+Newborn sized diapers, I recommend Pamper's Swaddlers enough for 2 weeks. We changed her a minimum 8 times a day back then! (If it isn't convenient to find them nearby, I'd stock up for a month + one size bigger, just in case).
+Wipes, I recommend Pamper's Sensitive
+Side snap shirts were our best friends (she was a summer baby) because I didn't have to put anything over her wobbly head. I recommend Carter's.
+NoseFrida Snotsucker + Saline drops in case of a cold and congestion
+White noise machine/maker/app
+Freeze meals in bulk for easy access to hot food for you
+Baby tub with a slant for hands-free bath time
+tons of soft washcloths
+NB bouncer or swing, the extra "hands" can be a lifesaver (especially if you don't have family close by to help)

@Mrs D: Sounds great!

I forgot, keeping those burp clothes near by are great for early on. For some reason when you lay them flat they often spit up.

One of the things I did that I have been so thankful for is getting a nice tupperware with a snap on lid for "Baby Medicine Kit". When she's sick, I know I can grab that box and everything is right there. I keep the tylenol and motrin, extra boogie wipes, extra paci, extra thermometer, neosporen, etc etc in that box.

Its also nice that if someone is babysitting, they can see the clearly labeled box and know where it is if needed.

We stocked up on diapers! We got some at our baby shower, but then bought some of our own every few times we went to the store. We didn't get any more than a few packs of NB diapers but ended up needing to buy more after LO arrived. We bought a lot of size 3's since I heard they are in those the longest. We only have 2 packs of size 4's (she isn't in those yet). We stocked up on wipes as well. We had probably 10 individual packs, a couple boxes and a refill pack. We got diaper cream, lots of soap/lotion at our shower, onesies, sleepers, swaddles, tons of blankets (too many), gas drops...

Here was our diaper stash when I was only 32 weeks. We added a lot more before baby was born and I'm glad we did. We had a different variety of brands, and some worked better than others but it was really nice to know we had the bare essentials stocked up when things got tight.

Good luck

We had:

One box of newborn diapers (around 250)

Two boxes of Size 1 diapers (around 500 total)

A box of wipes/refills (about 700 wipes)

Creams/ointment/etc.: Aquaphor, A+D, Triple Paste, California Baby Super Sensitive Everyday Lotion, California Baby Calming Shampoo and Body Wash

First aid: Saline drops/spray, nasal aspirator (NoseFrida), rectal thermometer, nail clippers, a general first aid kit (we had the First Years/American Red Cross one), gas drops, infant tylenol

A pack of 3 bottles and some formula samples that had come in the mail, just in case bf'ing didn't work out

Freezer meals: we ended up with about 2 weeks' worth. I wish we'd had some other quick stuff on hand like frozen pizzas, frozen smoothies, etc.