If you haven’t bought your pram/pushchair system yet, some of them came with free changing bags! The best ones for me (I had 3 children and 4 changing bags) were the ones that came with a little fold up changing mat. Handy for the back of the car/grimy kids changing station/picnic blanket at the park.
I would actually go against most advice given and buy one specifically for babies rather than a generic backpack- it doesn’t have to look ‘babyish’ but something neutral in blue/black. The extra pockets are just wonderful and they often have clips to pop onto the pushchair
I have had a satchel type silver cross one that came with the pushchair, good for bottle storage, had a changing mat and zippy space for snacks and some spare clothes but there wasn’t quite enough space for extra outfits. DD1 was a puker.
The other three were variations of this and I also bought one for my sister in law. About £20, backpack style but with MANY pockets and waterproof areas. Comes with the fold up changing mat (I always kept this loaded with a small pack of wipes, one back, mini sudocrem and a nappy- so if I was at soft play or something I could just grab and go) A space for phone and keys plus roomy enough for toys and extra clothes too!