Start gradually with age appropriate tasks. Little hands can help scrub small potatoes or radishes with a brush, tear lettuce for a salad (since the size of the pieces can vary), add cherry tomatoes to a salad, add the other salad items that you have cut, measure rice into a cup and measure water/add it to the pot. Slightly older kids can snap the ends off the green beans as you mentioned, without sacrificing most of the bean (LOL), work a salad spinner, separate celery stalks from the bunch, etc. I'd start at 4 for the first round of things I mentioned, maybe 5 or 6 for the 2nd group.
At any age, they can start putting things on the table like silverware & napkins, and even plates and glasses if they are not china/glass but plastic or something unbreakable. They can do the serving spoons, the salad dressing & ketchup, salt & pepper, etc. They can also return condiments to the refrigerator after dinner. In my mind, setting the table is part of "cooking and preparing" the meal.
By 7, they could use a safety knife to cut easy veggies like cucumbers or mushrooms. They make serrated knives for kids that work on many veggies requiring a straight cut. They can also cut up pieces of green pepper if you have cored them - those safety knives don't work well on a "curve" if you know what I mean. They're too hard for kids to maneuver.
By 8 or 9, they can cut more difficult veggies, like broccoli or cauliflower being separated into florets, peeling and cutting carrots, etc. They can try shucking corn although that is sometimes difficult. We always were sent to sit on the front porch with some ears of corn and a paper bag. I'm sure an adult finished off removing the remaining cornsilk but kids can insert the corn holders if you use those. They can also thread veggies onto skewers for kabobs.
Depending on their fine motor skills and skill with a knife, you can add responsibilities at whatever pace makes sense to you. Obviously they should be closer to 9 when you let them near the stove, turning on burners or stirring things that can boil over.
I think if you start slowly and simply, so they can be successful in small things, you can GRADUALLY add chores & responsibilities that are more challenging. It's more important that they be able to finish a simple task well than go to something too difficult. Keep it fun, compliment them for whatever they do, and don't make helping an option. You can start by letting them choose among 2 tasks - "Would you rather cut the cucumbers or wash the potatoes?"
I think it's great that you are doing this. If you can involve them in the shopping without making yourself crazy, that's usually helpful as they get invested in what they helped buy.