When my daughter was a toddler, she was fond of holding the broom. That gave us an idea to let her do some house chores like sweeping the floor and wiping dust with a rag. And then she progressed by doing small errands like giving me a glass of water. I remember her face, she was so proud after accomplishing something and that probably gave her the confidence in facing challenges as she grew up. Maybe that also gave her the volition to be good in school especially in grade school. Home training is very important to children and parents should not miss doing that.
If you have noticed that girl children are naturally attracted to do the household chores at very young age. Around 2 and half years they will start cleaning with brooms, dusting, wiping and playing with kitchen items. It is a good habit to encourage good behaviour and let them feel good about it too.
The rule we were told was to start by making sure they are things the toddler can accomplish and then get them used to it. We're slowly starting to introduce chores to ours, with something as basic as putting his toys away when he's done. He's not perfect because he gets distracted easily, and often forgets some but he's getting better and he knows that if he puts them away he can find them to play with easily next time. We'll move onto things like sweeping and setting the table when he's a bit older. I don't trust him not to run with metal utensils yet!
Making them pick up after their messes is good. My little sister makes big messes with paper and we tell her ''you can make as big of a mess as you want but you must pick it up.'' This is sort of a win-win situation. She gets to do what she wants but then later cleans up and saves us the work and she likes it like that. I wouldn't say that they SHOULD clean around the house if they don't want to because they're only toddlers but if they do, let them. It doesn't hurt anyone.