Our Homestead

Corn is easy and quick.
Almost like sunflowers, it grows very quickly and it's fun for kids to watch.

Not exactly a vegetable, but I'd want to add sunflowers here. They are great to gor for children because you can almost see them grow if you keep looking.
It's nice for kids to see progress.

radishes, for sure.

Radishes are great to grow for beginners. The seeds germinate within a few days.
They grow very quickly. You can eat them 45 days after planting.
Usually they don't mind whatever weather, wet or dry, but it's better wet than dry for them.
The seeds are not too small.
You can't mess up much. They will germinate if you plant them too deep or not deep enough.
They will grow if you put them close together and far apart.
Radishes have my vote of easiest to grow vegetable.

Beans, especially bush beans. You don't have to do anything at all.
Pop the oversized seeds in the ground. They are easy to plant because they are so very big.
Then just watch them grow.
Watch them flower, and watch the beans grow very quickly.
Pick, eat, and enjoy :)

Zucchini, it doesn't get any easier than that, and you can practically see them grow.
The plants get huge in no time and produce a very nice amount of zucchinis.

Hmm your post looks empty, so let me add.

Many people grow tomatoes which is surprising because they are far from the easiest to grow.

Peas are easy. The seeds are big, they can stand heavy frost, and they grow very fast.
The only potential problem is that they need a trellis.

Beans are also easy to grow but if you have pole beans as opposed to bush beans, you need a trellis as well.

Radishes. Oh yes, it doesn't get any easier than that :)

Cucumbers are easy too, if you have enough room.

Lettuce. Spinach. Mustard Greens. Not much to it.

Come to think of it, most vegetables are relatively easy to grow!