The Boots parenting club gives you a free basic changing back when you sign up to them. It's not the biggest bag, but it's top zip-opening (well there's a couple of slightly different styles, but I think they were all top opening). This was okay for us to get started and meant I could get an idea what I actually needed from a changing bag. We now we use a small old backpack because my partner can also use it while slinging our toddler on his front.
You couldn't get much cheaper than free to get you started at least