We just packed a light muslin blanket (baby was born in July) and two take home outfits, one in NB size and one in 0-3 just in case. The hospital will provide diapers and wipes, plain white shirts or onesies to wear while they're there, etc.
We brought a couple different sizes of take-home outfits. The hospital actually said for security reasons they have to stay in hospital attire. We had a whole diaper bag in the car ready, just in case..
Re: hospital