Westminster or Atlanta Classical Christian or Homeschool

If I can get Adelina into a good private school then I have no problem with sending her to school. I'm not against schools at all, just poor education systems! So, we are trying to get Adelina in at Westminster on a scholarship but when someone told me her chances are slim, scholarship or no scholarship, I started looking elsewhere. I found Atlanta Classical Christian School. Their tuition is somewhat affordable, $5800 a school year. Before you freak out Westminter is ~$18,000 a school year. Also, I've considered joint enrolling her in any school even a public one just to do extra curricular activities like foreign language, sports, band, orchestra, home ec, etc.