I have a Petunia Pickle Bottom touring tote for my small diaper bag. So far I have loved it. I comes with three different straps, so you can adjust how you carry it. It has straps that will attach it to the stroller.
My larger bag is an OiOi messenger bag and I have loved it too. So far it has had plenty of room for me.
I have a OiOi messenger bag and love it, even with 2 of everything it has tons of room.
I have a petunia picklebottom shoulderbag and love it
I love my Ju Ju Be Be All! Plenty of room, and not too bulky.