My four year old boy loves to help, though similar to Jennifer's daughter, that can be more of a hindrance in reality! But I think it's all part of developing a healthy attitude towards being helpful and pulling his weight around the house so I encourage him.
I don't like those lists that circulate saying "these are the chores your child SHOULD ne doing by this age" as partly I dislike anything so prescriptive and partly I think each child and family is different, so you should work with who you are and what your circumstances are. I think an ad hoc approach working with your child's enthusiasms is best.
As for rewarding with money, I would not and will not do that. Not for every day, mundane stuff around the house. Maybe if it's something out of the ordinary but the usual things that have to happen so the household functions, everyone needs to pull their weight and muck in to do those and the reward is that the house is clean, there is food to eat and clean clothes to wear. Just like for adults.