If you've read my bio, you'll know that I've taught martial arts since 1993. A long time. Most of the classes that I taught were kids classes. For most schools, kids make up a large percentage of the population. Parents think it teaches them respect, discipline, self-defense, and a whole slew of stuff. As I've stated in my bio, the stuff we were teaching was just crap. Let me explain briefly. In all of the classes, both kids and adults, there was little physical contact. Not that I want to touch people, but in order to train for a possible physical altercation, a fight, you have to train with a training partner. Our school did little of that. Worse, all of the self-defense techniques were done in the air. Students didn't feel what it was like to hit something, which is an important concept in martial arts.
For me, there are a few things I look for when I go into a school. Are the teachers egotistical? Some indications questions to ask.
Do they display a ton of trophies? A few is fine, but if there's a lot, then red flag it. If you're confident, there's no need to show off.
Do teachers treat students like people? It's a privilege to teach anyone because a student must open themselves up to their teachers in order to learn. I had a student once where his teacher made him lie face down and pressed his face to the floor with his foot. This student was nice as can be. I went to the school to check them out, and I could read their huge egos. I've had other students hit on like in a bar by instructors. That happened often in my school even by the owner.
Ask about partner drills, bag drills, drills that will teach both reaction and striking skills. This is a must. Most MMA schools will have this. Other traditional type schools may not.
Look at the cleanliness of the school. All schools smell like feet. Don't judge based on that. I'd focus on whether the school is bright, clean, and organized. It reflects on the teachers and owner of the school.
I'd also ask about how the belt system works, how belts or rank are earned, and if they offer one-on-one sessions. A really good school will offer a number of these sessions for free. It shows they care. If they don't, ask for them as part of your negotiations.
The overall feel should be positive. You should feel that you can learn. The most important factor is choose something that you'd have fun doing. I've not gotten in a fight since I started in 1993. I don't plan to. Fun is going to have a huge factor in your improvement both in physical and mental health.