I also use a backpack style nappy bag. As I rely on public tranport during the day and sometimes need to do a fair bit of walking it is much less of a hassle than a shoulder bag.
I also have large pockets and a basket as part of my pram, but that space is always reseved for my shopping!
I always carry:
-3 spare disposable nappies (and more if we are going away for the whole day/night) (can I just add you will probably need to carry more nappies on you for a newborn)
-Nappy sacs
-3 bottles of cooled boiled water (1 of them to be used for drinking water),
-2 seperate containers with the formula measured out (I am still to get one of those divider formula containers!)
-container of fruit/cereal
-wipes
-nappy rash cream
-change of clothes
-hat
-teething gel/drops
-dummy
-2x toys
-at least 3 bibs
-bunny rug
-Aidyn's health record book
-wallet, keys, phone, makeup, tampons, plus a million receipts and other assorted junk, LOL 8-[