Firstly, congratulations.

You might want to consider a changing wallet like this Skip Hop one which you can just pop into a larger bag. For air travel I found a classic diaper bag too small to take everything I might need (clothes, milk, water, snacks) but too large to use in an aircraft toilet comfortably.

Instead I like to use one of those large Longchamp folding bags and put in the Skip Hop changing wallet and several ziplock bags for clothes, food, toys, additional diapers etc.

However, I do like to have a classic diaper bag that is always ready to go to use when space is not an issue. I have a JuJuBe All in plain black which either parent is happy to be seen with - it is not a fashion accessory. It has had a hammering over three years and withstood it pretty well although the changing pad is a bit sad now and I've struggled to get a reasonably priced replacement pad in Europe (ok in USA).

It is useful to have a diaper bag where you can easily get the changing pad out one handed, with bag on your shoulder and holding your baby (think public toilets, not got pushchair in toilets with you and no space where you want to put your bag down). Separate pockets in one big pocket where you can easily see everything at once is also good (hence suggestion of ziplock bags if you are using a larger bag without pockets).

If I'm on a quick outing I might just pop the changing wallet in the pushchair and not bother with the diaper bag.

Enjoy the diaper bag shopping!