Four-gallon rigid-plastic square buckets can often be found for free (although sold online for $5 and up). Try local restaurants, as they often buy frozen fruit or other foods in these containers. I’ve found these to be super useful for carrying groceries. For several years, they’ve been my regular totes. Unlike canvas or other sacks, these can’t leak, stain, or tip over easily in the car. They have a handle. You can load them up with heavy bottles or cans and still easily carry two pails. If there’s a spill, they rinse out. Not in use, they stack. In the store, a nested pair fits on the lower level of the shopping cart. I shop fairly often, so I usually don’t need more than fits in two pails, but one can always drop a couple cloth bags into a pail, for additional carry space, using the pails for the heavier items.
On car trips, they make efficient use of space, packed with rainy-weather gear or various other categories of supplies. They are easy to move around when rearranging things or carrying to and from the car.
They often come with square lids, a little fussy to snap on and off, but not necessary for shopping. With a lid on, the container is weatherproof for use outdoors. I’ve camped with a small tent, and stored things in these buckets outside the tent.
My suggestion is to get some for free.