Hi, I have had 3 little ones, now 7, 3 11/12ths and 16mo. I can tell you the main things you need are nappies in a bigger size, johnsons wet wipes are excellent and get all sorts of stains out, including off of sandshoes and chocolate paddle pops.., cloth nappies for all sorts of spills and a baby carrier like a baby bjorn, these are priceless. A good quality pram that you can maneuvre around the supermarket with a decent underneath, and a big pram for walking outside, you'll need fresh air at some point!
Singlets with press studs are also great for winter and you can never have too many of them, although buy white because you never want to put blue on a girl an vice versa...
Hope this helps and good luck, you'll enjoy your new life!!!