This is my current shopping setup, from a photo taken today. I picked up the big paniers off craigslist. The don't exactly fit the bike, but they work fine wedged into the existing back rack, with an automotive hose clasp of all things used to secure them. The tension of the load forces the basket to ride more securely and it hasn't fallen off or come loose yet after a several dozen loads. The beauty is I can remove the whole thing by simply taking off the hose clamp and lifting it off the back rack. I think almost anything can be secured on a bike with hose clamps, brass shims and duck tape. A brass shim has been keeping my shifter in one piece for months now.
The paniers carry a ton, plus I can use the back rack to carry more if needed. Between that, the front basket and my backpack I can haul more on the bike than I ever did in a car. And I can carry the whole vehicle including groceries right to my door.