Choosing a Marshal Arts Instructor

Who teaches the classes?
Some facilities will use more experienced students to teach classes.
Are your classes mixed with children and adults?
If you are an adult you many not want to be "slowed down" with children in your class and conversely, you may not want your child training with adults.
Do you participate in tournaments?
This is not a right or wrong answer but a matter preference. If the focus is on tournament participation, much of the time and effort will be spent in preparation. If this doesn't interest you than perhaps you should choose another instructor.
What style do you teach?
How often are the lessons?
Can I come in and train at other times as well?
Do you have belt test fees?
This is an additional fee above what you pay for the lessons. You should know all the associated cost of the program.
Do I have to sign a contract?
A contract isn't a bad thing but be clear that you understand the cost, the length of the commitment and the circumstances (if any) under which you can terminate the contract.
What is the cost?