Well at my hospital they pretty much provided with most essentials for me like the pads, underwear, witch hazel pads, numbing spray, bath towels, socks & diapers.. But yeah..
For you; shampoo, body soap, going home outfit, maybe some slippers??..
For baby; going home outfit, one or two baby blankets, hat, mittens, socks

I packed snacks a few outfits shower stuff and a blanket and a few comfy clothes for me