This is the most common dilemma faced by WCI readers. There are some clear answers, but even when the answers aren't clear, these important factors will help you to arrive at the right decision for you.
Public versus private school is an endless debate, but only because no one ever adds in the opportunity cost, at which point many will realize it is a luxury that they either cannot afford or don't value sufficiently to buy.
Don't make the mistake of putting all your resources toward college savings at the expense of retirement savings. It'll likely come back to bite you.