My family did a lot of moving around when I was in elementary school, but I think this is how it went.
Pre-school and Kindergarten: private, in Kansas
Grade 1-2: I was in England, I went to a special private school for American students
Grade 3-5: Public lower school, at my current home in Washington (finally stopped moving around!)
Grade 6-8: private middle school, 30% acceptance rate (lucky to get in!)
Grade 9-12: Same private school, I am currently in 10th grade. I absolutely love my high school and you would have to fight me to make me go to another, but it is somewhat pricey.