I also have a list in my journal entries that I'm going by, if you'd like to check out the items on that!
For baby: hospitals will usually provide diapers and wipes until you go home. Some hospitals(I know mine does) also provide a breast pump and bottles if you plan on breast feeding, and formula for formula feeding. Depends on how long you're staying for, I'll be staying for three days. Make sure to bring a few onesies, a going home outfit, hat, socks or booties, mittens, swaddlers(some hospitals provide them but not all) and a car seat.
For you: bring a couple change of clothes(comfortable), comfortable big underwear, shower/hair/makeup products, paperwork you need, money, phone, phone charger, something that makes you feel comfortable and at home(framed pictures, stuffed animal, blanket, pillow, etc), snacks, something to pass time if you're not tired and not catering to baby(book, laptop, movies, etc).