Some people have mentioned that you will receive certain things from the hospital. Just remember that all hospitals will provide different things. I'm an OB nurse. The hospital I work at provides t-shirts and blankets for use while in the hospital, but they are not to be taken home. Everyone gets a black diaper bag full of goodies that's provided by Enafamil or Similac. The bags for breastfeeding moms include an insulated bag and reusable ice pack, and a couple bottles for breastmilk storage. Of course the nasal aspirator is meant to be taken home, and we also provide a digital thermometer. We provide enough diapers and wipes for the hospital stay, but there's not much left when it's time to go home. We put triple dye on the baby's umbilical cord, so our patients don't have to use alcohol on the cord at all, just keep it clean and dry. For moms, we have Lansinoh, Tucks, and Dermoplast, but they're part of your pharmacy charge. The pads we have are absolutely huge. I preferred to bring my own Always overnights longs. If you wear the hospital's disposable mesh underwear, don't remove the liner on the pad that exposes the adhesive! Your hair will stick out through the mesh and stick to the underside of the pad, and it will be very painful to pull your underwear down the next time you have to go to the bathroom! Not pleasant! As far as the breast pump goes, ask to pump in the hospital. The pump kit can be taken home and used as a manual pump (though not my favorite one, it will do in a pinch) and it will give you a chance to try out the hospital pump and see if you want to rent one. I preferred the Avent hand pump because I could use it one handed, never needed an outlet, and I controlled the speed and strength of the suction. Personally, I just felt like a dairy cow when I tried the electric ones! I also liked the Avent bottles best because they were much more similar to my breast shape, so the baby didn't have problems switching back and forth.
I definitely recommend a swing. DD#1 didn't like to be held, and was only quiet when in her swing. DD#2 liked to be worn in the sling most of the day, but was still content in the swing when I needed to put her down. I used a pack-n-play with a bassinet insert next to my bed during the night, and the bouncy seat for naps downstairs during the day. Your heavy blakets will be good for laying on the floor to put the baby on for tummy time, or laying on the grass for playing outside. I used to lay a blanket on the grass in the shade and put the baby in the swing or bouncy seat on the blanket, so if a toy or pacifier got dropped, it landed on the clean blanket and not in the grass.
Another thing you'll want to get soon is some type of tote for toys. Even though the baby won't be using most of the toys quite yet, it's nice to have a place to put them all. A zippered lingere bag for the washer is good for baby socks too. I can't stand seeing babies with bare feet in public, so to hold the socks on I got some soft crib shoes that tied with laces. They're not restrictive, but they stayed on perfectly and were much cheaper than Robeez.
I never used a Boppy. I'm short-waited, so I didn't really need to lift the baby to reach the breast. I also never used a diaper pail or a changing table. As you can see from all the responses, everybody likes different things, and after a few weeks you'll decide what works best for you!