In America, parents have (almost) always had the "right" to choose a good school for their children... However, some of those choices have been much more expensive than the free ones offered by the state, but those expenses have "bought" a lot more parental freedom and discretion regarding their child's education.
I am writing from outside Arizona, and I don't know the details of the school you mention or the expenses attached. So, here are some generalities to look for:
1) Pick a school that conforms with your worldview as much as possible. The school, teachers, and student body you pick will be influencing your children nearly as much as you do!
2) Pick a school that you can afford... it doesn't have to be "cheap" - but it must fit your budget.
3) Don't ever expect the school to "do it all." You are still the parent and responsible for your child's education. Be involved!
4) Every school integrates one or more world-views. Public schools teach from a secular worldview and some religious schools intelligently and meaningfully integrate their religious view within each class. Math, for example, is taught in a way that helps kids to have greater wonder and appreciation for God and his concerns regarding math and its uses. However, many (most?) religious schools tend to mix their faith with secular educational practices. In other words, they reflect a religious environment while teaching basically a secular curriculum. Find out how your school "integrates" faith... Does faith effect what and how each subject is taught? Are faith commitments active or passive in the school? Does the school have goals for spiritual growth or does it just provide a comfortable spiritual environment?
5) How does the school address the special needs of students? My family had to leave several Christian schools because they made no or few provisions. Also, those willing to make provisions often lacked the understanding and the resources to make adequate provisions.
6) Finally, are all children "loved" or are they just "items" in the education business? This question is relevant to both teachers and administrators. I find many teachers want to engage their students, but the pressures put on them by administration (in terms of class size, testing, "paperwork", inservice, etc.) can steal the moments of time interpersonal communication requires.
Summarily, find a school (or make a homeschool) that fits your family's beliefs, goals, and your child's abilities. I have friends who took their kids out of the best "college prep" school in town because they were losing their childhood time to afternoons and evenings filled with homework. On the other hand, I know families of academically gifted children who left schools that were geared to an an average academic level. We need all kinds of schools to meet the individual differences of families and children. Make a wise and prayerful decision... and be willing to change it as the children grow!