I'm not in favor of restricting at all the people they can vote for. Let them elect an Iraqi toddler to be US president for all I care; if they're the ones taking care of us, they probably have a good reason.
Just as a thought experiment: what if the threshold for having a vote was tied to paying a positive amount of personal income tax, and the weight of each vote was proportional to the amount paid? How skewed might such a system be? My first reaction is that in countries with high inequality, the wealthy would disproportionately influence the outcome. However, on the other hand, if people avoid or minimize paying taxes, they would lose the power of a weighted vote, which theoretically could incentivize paying taxes in full.
Right now, the top 10% pay about 70% of federal income taxes, so your plan would effectively make 90% of the population's votes effectively worthless.