I used a pink lining bag when the children were smaller but tbh I found it really bulky (not great with a double phil&teds) so now I use a small Cath Kidston bag, it's fits in 4 nappies, wipes, changing mat, wetbag, juice, purse, keys, phone and snacks.
Although I don't use one now (only I need to take spare clothes and that get shoved in my handbag!), When Ben was in nappies I used a OiOi Hobo for shorter trips (always had plenty of room in it), and if I was out for the day I invested in a OiOi Carry All Which I could fit LOADS in I've kept them both for when I get pg with number 2!
My favourite is my Ju Ju Be Right Back. It is perfect for organising everything, holds enough for a full day out and is a neutral enough Brown and pink so DH doesn't object too much to carrying it for me sometimes