I think there a merits to all three systems if done correctly. Research shows that smaller class sizes are advantageous- and most private schools offer smaller classes than most public schools. However, I'm not sure it's worth the extra cost, unless you've got a lot of money to throw around and the school is known to be better than public in the area.

I worked at a private school for kids with learning differences, and the students definitely received more individualized attention, they had the best resources, etc, but it cost $25,000/year. I've also observed at lots of public schools (I'm going to school to be a teacher) and I have to say I'm impressed with a fair number of them too. Money doesn't buy a truly caring, compassionate teacher, which sometimes can make all the difference.

I think home schooling could be good, with the right parent and the right child. But, I think socialization is very important, especially for young children, so you'd have to make sure they get out enough with kids their own age. My cousin home-schooled her oldest daughter for a few years, but the girl didn't have any friends except her younger sister, and now she will not even talk to kids her own age. She is incredibly smart, but she is completely silent in school. Luckily, she goes to a great school that tries to help her out socially, and recognizes her issues.

I teach a lot of home-schooled kids piano. Some of them seem dedicated to their school work, some not. One kid I talked to today said his parents were thinking about sending him to public high school because he procrastinates and didn't listen to his mom like he would a teacher.

I guess the best thing would be to compare schools in your area, and decide what you feel is best. It's good you are thinking about it early- it's an important choice!