We are getting a messenger bag this time around, probably the JJ Cole system 180. With our foster kids we had large and small traditional style diaper bags. When we only had one kiddo, the small one was great and convenient. We'd just throw in a few diapers and wipes, formula and bottles (so glad we won't have to worry about that with our own!), a change of clothes, and a receiving blanket. For larger day trips we would take the larger bag. When we had two kids we would use the big one and usually have snacks, sippy cups, twice the diapers since the toddler was still potty training, etc. We could fill it up easily! It was too big to fit easily under our stroller, and we didn't have a good carrier, so we used the stroller a lot. We still have the small one, but the large one was destroyed by the time we were done with it.
We talked about a back pack, but I really liked having the bag on my side so I could grab a receiving blanket or burp cloth easily when I was holding the baby, or get something out for the toddler. It was really hard to keep both straps on your shoulder. We are hoping the messenger bag is the best of both worlds! Neither of us carry a purse, so it doesn't have to be big enough to throw that in, and hopefully the slimmer design will fit in our stroller better.