The best martial arts class for kids are the classes that they go to. If the child does not get to class it doesn't matter what the school's credentials are.
The parent starts the training by committing themselves to the classes. The parent delivers the child at the door several minutes BEFORE the scheduled start time; give the kid a chance to settle down and get ready for training. This shows the child that you respect the Sensei and value what they are teaching your child while showing the child how to be punctual. Stay at the dojo during class (don't treat it like a baby sitting service, your child will know). I recommend a podcasts and audiobooks while you watch the class.
Which school? You, the parent, will be spending several hours a week at this place so don't minimize your due diligence. The correct answer could very well be there isn't a place with classes that matches your schedules at this time.
Parents should ask around and see where their friends are going and also where there friends have stopped going. Ask why.
Parents should first attend/watch a class that their child would be attending. Leave the kids at home for the initial visit so you will not be distracted from your all important task of managing the development of the child. Arrive 15 minutes early and stay a few minutes after the class so you can experience the way the school is run. Your gut will tell you which schools will be good for your child, listen to your gut.
Talk with the chief instructor and the person (teenager?) who will actually be working with your child. Would you feel safe leaving your child is their care for the weekend? What is the instructor teaching? A parent should watch to determine this, do not base the molding of your child's mind on what you read in a brochure or on the web.
After making your choice(s) of potential schools attend a second class with the child. This time observe your child and dialog with them about what is happening.
At 6 years of age the style doesn't make much difference. The instructor is what is important, not the brand name.