This is a link to my favorite. I carried my youngest in this carrier until well after his second birthday. It's also nice because he's on your back so he's not getting into everything. Plus baby wearing supposed to be good for them, right?
Dedicate specific toys for the car and shopping trips. Only let him play with those toys when he's either in the car of the shopping cart. I would also use a sling or kid backpack during this stage to keep them truly contained.
You could also make a shopping list for him with pictures of things on your list for him to help find. Keeping him distracted will keep him contained.
Or do everything you can to NOT take him shopping until he's a little bigger and more willing to hang out.