Please update your question and clarify, are you asking what curriculum is best or which charter/private/virtual schools?
Personally I would not use any charter or academy that is funded by the government or public school system. Connecting Waters, K12, and a few others I know of are funded by the public schools. These kinds of schools typically pay the members for curriculum and classes. But the member is signing away their religious and parental freedom when they accept these kinds of monies.
The whole point of homeschooling for many of us is to veer away from the control /indoctrination of the schools and the anti moral values and attitudes that they so wrongly portray to the student as desirable.
So my answer would be to set yourself up as your own private school. Check online for the Illinois state homeschooling support site. Some states require you to register an affidavit with the state dept of education. Your Illinois homeschool support site should tell you everything you need to know to make that happen. Sign up with HSLDA. Also, 'yahoogroups.com" should have a listing of homeschool support groups in your area (also check craigs list, meetup.com, etc.) These groups are usually free and have an e loop where people can post up coming classes, field trips, and park days. You can ask questions on these sites for curriculum and material references. You didn't say weather you were religious or not, but if you are,
some of the better curriculum in my opinion are: Apologia science and Rod and Staff English series (may need to start at lower grades because it is advanced.) I like Chalkdust for math.
Mail me if you have questions,
Gail
(homeschooling 10 years.)