I bought a nice rucksack from Kipling (which was more expensive than it needed to be, but it looks nice): it can be put in the wash (it is canvas), is reasonably water-resistant, has good compartments and is very roomy for not being too big. A bit of a pain with my big pram, as I needed to get a velcro tab to hook it onto the handlebars, but with the foldy pram the back straps just went over the handles.
The front compartment has changing things - mat, nappies, wipes, cream, antiseptic handwash. The back (larger) compartment is for wallet, keys, drink, biscuits, etc.
The rucksack style has spared my back (I had to stop using the messenger-style bag that came with the Pampers- and it wasn't that big, either) as my bag was getting strained. Also messenger bags tend to swing forward and tangle with what you're doing!
I have a very active boy, so am the mother charging about the park with everything she needs right on her back!
BTW, I have found that buying (new or 2nd hand, doesn't matter) changing mat liners is a decent alternative to a changing mat for a changing bag. They are long enough for a littlun, absorbent (terry on one side) and water-proof on the other side (some sort of nylon/plastic). They roll up small and can be washed. I think they are 2 for £7 at John Lewis.