We gave our Jr. high/Sr. high kids money each month and that was expected to cover their lunch money (if they didn't want to pack their lunch), entertainment activities, some clothing or anything else that we felt was unnecessary thus making it something they would have to save up to buy. That relieved the number of times where they were coming to us for money for this or that. It also made them consider how they wanted to spend their money and think about budgeting or at least their priorities.
One mom in the group said that she has a list of chores her son can do during the week and turn it in to get paid on Fridays. But in order to get that "extra" money, he must keep track of what he's done by writing it down and bring it to mom on Friday or else it's forfeit. Again, putting the responsibility more on the child than mom & dad. What I gathered from hearing the mentors speak is that we don't have to choose one way or the other (paying for chores or giving an allowance). We may need to implement a combination of the two approaches. Big picture: we all want our kids to know how to handle money in a responsible way. They need to have some money to begin learning how to budget, to save, to give so that when they are older those principles will be well established. And maybe for now that looks like a small allowance and a little extra pay for taking initiative and helping out with some stuff around the house.
Home school was not very prevalent when the mentors were raising their children, so most said that the choice was primarily between the public school system or private education.