For short outings I've just put a couple diapers, paper changing pad and wipes pouch in a basic messenger bag like one of these (all either bags I've owned or seen rec'd here). If I had extra space I'd add a small wet bag, burp rag, and change of baby clothes in case of blowouts. Part of your space needs will depend on whether you're breastfeeding or need to carry bottles. You'll also need more space if you're cloth diapering and these bags will probably all be too small for cloth dipes.
I used the Ergo's front pocket a lot when just running into the store for a few minutes and had the rest of the diaper gear in the car. It was fine for a small wallet, keys, couple tissues but wouldn't last for much longer than a quick shopping trip where I was willing to cut things short or go out to the car for a diaper change.
I don't have any great ideas for the several hour walking with a carrier trips and always struggled to find a bag that could last that long without straps digging into my neck or feeling too heavy while carrying baby.
ETA: I'd start small with one bag that will hold a medium/large amount of gear like a Skip Hop or a backpack and one bag for babywearing like the ones listed above. You can always shop around or order a few to try on Amazon after baby arrives and once you get a sense of how much gear you're actually hauling and what styles of carriers work best for you--slings, Moby, Ergo/Beco, etc.