Here's my list for baby at hospital, which is pretty much my list for the first month, apart from volume of things. Embarrasingly, my own list is much longer...
5 times babygrows
Hat, newborn Gap triple roll socks as scratch mittens as they are the only damn thing that stay on. Newborns really can scratch themselves.
Warmer layer of clothes.
Newborn nappies
Muslins
Cotton wool
Swaddling blanket, which also helps cut down scratching.
Wrapping blanket (fancy wool one grandma knitted)
Cuddly toy grandma knitted as I can't help myself...if you have to leave baby with anyone else (eg in nursery or NICU, its nice to give them something that smells of you. So I'm already occasionally sleeping with this toy )
Car seat
Pen and paper (for taking notes and numbers)
Handful of spare plastic bags for chucking and carrying things.
I won't bother with bottles, milk etc as I'll wait and see how we get on. The hospital will have milk in ready made bottles if needed. After that we can get stuff alomost 24/7 in london, so thats's what we'll do.
I use olive oil in the first instance for all things baby skin related, will take it from there if needed.
My extra newborn recommendation is a fleece. you can whack it on the floor in any room and pop baby down flat. highly portable, easily washed if needed.
in fact, we took ds1 to gozo when he was 11 weeks old, and i rolled the fleece up, tied it with a dressing gown belt and kept it over my shoulder as hand luggage. so i could pop him down on any surface to lie flat when waiting for planes, choppers, in restaurants etc, and on otherwise hard surfaces. Plus the hotel cot mattress was dubious, and this made a handy barrier to any lurking germs.