It will depend upon what martial art you wish to study. In most cases, the best place to study a martial art is the country where it originated. Karate would be Okinawa, Kung Fu -> China, Tae Kwon Do -> Korea,
Most people do study in their own country, but some people can afford to travel and experience life in other countries. This is helpful in many businesses where you will need experience with other ways of life.
in most areas of the country, middle school starts in either 6th grade (when most kids are 11 years old) or 7th grade (when most kids are 12 years old). Some places have it starting in 5th grade when kids are 10.