After trying a few different styles of bags and backpacks, we ultimately settled on using this backpack most of the time. Diapers in the small front pocket. Bottles in the front main compartment, along with other snacks. Clothes in the back compartment, perhaps with some small toys. Wipes on the side.

We had a big messenger bag style diaper bag, but it was too awkward to use. The backpack is a little smaller, but with careful packing does pretty well. When we were going out for a longer period of time, I'd sometimes just use a duffle bag.