Between my three kids, they have attended private kindergarten, six public schools, a magnet school, a private Catholic high school, a private Christian school, an online school, dual enrollment, AP, IB, public universities, and been homeschooled. Next year one will start at a private university, so I think we will have hit almost all of the options at that point.
My advice would be to determine which options are available to you in your area, rule out those that you believe are unaffordable, then choose what you think the best option is for your kid. Note that different kids can do better at different schools - my middle son is at an IB high school, but his younger sister is attending a Catholic high school. He likes the smaller school size and the challenge of the IB program; she wanted a larger school with an orchestra and choir.
Mostly my kids went to public school until high school, then they all went to private schools for different reasons. One was for efficiency and misophonia, one was for ADHD, and the last was for personal safety. (I guess I have sensitive, delicate children, LOL!) One is likely to end up at a private university out of state, the other two are/likely will be at in-state public universities. Again, each has different needs and plans.
On cost, I was talking with a friend the other day who paid for both of his kids to go to private Catholic schools from K through 12, and they told their kids they were on their own for college because the parents were basically tapped out. Also, their retirement is behind schedule according to him. So if you want to help your kids go to college, consider how paying for private K-12 school now may impact your ability to help them later.
Once they get to high school, I'd encourage you to start talking career plans with them. With my two younger ones, we took them on "high school visits" to their available and affordable options and involved them in the decision. It worked well in that the kids were a little more committed because it was their choice as to where to go and they know it is costing some money from their education funds to have them attend.