The rack that came with my bicycle is fairly low quality. An aluminum thing that uses twisted-plate supports. Good enough for shopping, though. I keep my Wald pannier baskets, as well as a third basket, permanently attached to it and just remove the whole thing when I want to use the bicycle for something else. It's only four bolts to undo. I also have a couple of wire baskets on the front/rear racks of another bicycle, which has a lower capacity over-all, but are necessary for various tasks that the Wald pannier baskets aren't suitable for, such as plates of takeout food.
As for how I shop with them, I just simply put my groceries directly into the baskets. I keep regular re-useable shopping bags folded up until after checkout. Also have one insulated bag for stuff that needs to be kept cold. After checkout, I find a place in the store where I can organize/balance my load. After it's all packed, I wheel out the door, get on and ride home. BTW, a bicycle is much easier to steer while shopping than a shopping cart is.
