We have all had the inconvenience of having to drag our child to the store who then proceeds to break down, have a meltdown, pull an apple from the bottom of the pile and in general embarrass us and cause mayhem. However if you want to share with your kids the attitude of enjoying their meals and want to impart to them the knowledge of where their food comes from instead of just having this incredible chore that you have to feed them five times a day, it is still a good idea to take them to the store every now and then, after they grow out of the Baby Bjorn.
Involving means engaging in the whole process, so see if you can get children to add items to your list before you get to the store, or read a label to compare items, or find a new item, or follow up with washing / preparing / eating what was purchased.