Get your children interested in gardening by letting them grow their own vegetables. There are a number of easy-to-grow vegetables that are suitable for growing in pots.
Radishes are the easiest and they grow quickly, which is a plus when dealing with children. Radishes are ready to eat in about 30 days (if they aren't pulled up sooner!)
Carrots are are another vegetable that is easy to grow in pots. They work well when planted with the radishes.
Chives are my personal favorite. I love the flowering tops and I like to put chives in just about everything! If your kids won't eat radishes, they may enjoy growing something, like chives, that you can use in cooking.
You may be able to interest older children in growing flowers in pots in their school colors if they aren't interested in vegetables!
Just about any pot will do as long as it is at least 10 inches in diameter and about 12 inches deep. Plastic pots work best as they don't dry out as quickly. You can even recycle an old plastic bucket, or something you have on hand. Just make sure the container has drainage holes in the bottom.
Put a small layer of gravel in the bottom of the container, or cover the hole with a few layers of coffee filters to prevent the soil from washing out; then fill with sterile compost mixed with topsoil. It's easiest to just buy a bag from the garden center.
Keep the containers watered and feed the vegetables every two weeks.