I don't know if I can call it the best out of your list, I am biased against Louisiana due to a month I spent on Fort Polk, but I live to the south west of Kansas City in Missouri and have to say it is a pretty good place to live. And I can give you some insight that may help you make a decision.
The support for homeschooling is pretty good, we did the home school thing from K through 8th grade. When it was time for high school we decided to go with a private academy. But that was due to things other than state laws.
As long as you stay out of KC and St. Louis I think you'll find your politics match the locals. That is an issue though, for anything big, KC and St. Louis tend to dominate, and they are much bluer than the state as a whole.
Based on your price range and land wants you would be pretty far out of the KC area. But since you have flexibility you can look near Joplin and Springfield. If I wasn't tied to a job in KC I'd be looking to move closer to Stockton Lake. If you like being on the water it is wonderful. One thing I will note if you decide on Missouri, consider getting 20 acres of land. Everyone I know, myself included, that got between 1 and 10 acres wishes they had gone for 20. The reason being that 20 acres is when you can qualify for agricultural zoning for property taxes, farmer deer tags, and other advantages.
If you have any questions please let me know.
*Edit* One thing I forgot to mention. The state currently does have an income tax but there is work going on to eliminate it. I'd like to say it has a good chance of happening, but as I said, KC and St. Louis dominate on the major issues. So I'm not optimistic.