There are state schools in the majority. Some schools are in ecclesiastical sponsorship but awarded the state-recognized degrees. There are some private schools that charge different levels of school fees.
In BW, the choice of secondary school takes place already after the fourth grade, as a rule, the children are at the age of about 10 years old. You will find the information in the age group 6 to 12.
At the age of 12, a change of school will take place only if the child is unable to cope with the chosen school.
You can find more information on the school system in BW at http://www.bildungsnavi-bw.de/schulsystem