I was a cheapskate and just got the basic target store variety. It was definately not large enough when my DD was newborn!!!! If we went to the city for the day we had wetbags stuffed in the bottom of the pram full of dirties cause it just wouldnt all fit!
Also mine is pretty heavy when empty so with the weight of all the clothies it is really too heavy to hang on the back of the pram with a tiny bubs weight in front. My advice would be one a bit softer so you can squish and fossick in it and not too heavy.

As for the other stuff:
One or two wet bags big enough to fit around 5 or six wet ones in for big days out. I have Jam tots ones which have snaps that let you hang it onthe pram or attach to each other.

A small wet bag for your clean cloth wipes. In my tiny bag which lives on the pram I just have a ziplock bag but in the big proper nappy bag I have one I sewed with waterproof fabric and a velcro closer. You can get them online from MCN stores. Oh, in it I have around 5 wet cloths.

I also have a spare snappy for terry squares when I forget to pack one, a changover nappy cover, a tiny bottle of hand sanitiser, one of those sample pots of sudocreme for the bum, a few of those disposable nappy sacks in case my bag gets full or leaky or if there are vommity clothing. Umm, purse pack tissues, a toy, emergency change of clothes, chewies for me, and Nappies gallore!
You see why my bag is too small? LOL