I've packed a 0-3 months with a pant and hat that came with it, non scratch mittens, 2 swaddling blankets (just incase), and a warm fluffy blanket. All you pretty much need is a towel, and a change of clothes (if you do plan to shower at the hospital). I know the hospital will probably provide these essentials but its up to you if you want to bring these stuff also like shampoo, toothpaste, and tooth brush and whatever you're missing just have who ever that's with you to run back to your place to get it.
For baby I packed a newborn outfit and a 0-3 month, hat, mittens, socks, and a blanket since it'll be cold. The hospital should provide everything baby needs while you're there (diapers, wipes etc)
They have these 30 packs of facial wipes at big lots for $1 and oh my gosh they're amazing. Since you'll probably be sweating a bunch I would recommend getting some! I got the green tea extract ones, they smell so nice. And any other stuff to make you feel more human. For baby you really only need a couple outfits, for varying weather possibilities. And of course the car seat! And I'd bring a swaddling blanket, and maybe some diapers and wipes if you want to save a little money, or if your hospital will even allow that.
At my birth class they recommended chapstick and lotion, which I wouldn't have thought of.