With a lot of choices available in Martial Arts, every year gets tougher and tougher to make the right decision.
The decision regarding the school should meet with your individual goals
Most common goals include
Self Defense
Fitness
Mental Wellness
Socialization
Family Activity
Sport
Then you should factor in your personality
Instruction type you respond to the best. This is not just positive/ negative reinforcement, but also if you prefer methodical, energetic, relaxed, pressuring, assertive, supportive, formal, or casual.
Your body type may make certain martial arts easier than others. If you are built like a fire hydrant, then Judo or Wrestling might come more naturally. If you are tall and long, striking may be better. All martial arts work regardless, but some body types have better success in certain sports
Your preference. Do you like sparring? Do you want to just hit pads? Do you prefer no contact and just want to do forms? Do you want an easier pace or a grind? Do you want to work weapons?
Big or small classes can make a difference. Some people like the energy of lots of training partners, and like to blend in so they aren't having anyone watch them too closely. Some prefer just a small tight group of people with lots of personal attention.
Price Range matters. You can spend a lot on martial arts. Know your budget before you start. Make sure when you talk to instructors, you factor into the price equipment, testing fees, dues, tournaments, and other add ons. A lot of places out there will nickel and dime you to death so be careful.
Before you can pick your school, start by looking at different arts and see what style lines up with your likes and dislikes. I've scored these on a 5 point system with 5 being the highest for metrics in Fitness, Self Defense, Community, Wear and Tear on the body, Tradition, and Ranking / Promotion fulfillment
Boxing - Fitness 3, Self Defense 3, Community 2, Wear and Tear 3, Instruction 2, Tradition 1, Ranking 0
Muay Thai - Fitness 4, Self Defense 4, Community 2, Wear and Tear 3, Instruction 2, Tradition 2, Ranking 0
Taekwondo / Karate - Fitness 2, Self Defense 3, Community 5, Wear and Tear 3, Instruction 4, Tradition 4, Ranking 4
Judo - Fitness 3, Self Defense 4, Community 4, Wear and Tear 5, Instruction 4, Tradition 3, Ranking 3
Kung fu - Fitness 2, Self Defense 2, Community 2, Wear and Tear 4, Instruction 3, Tradition 5, Ranking 3
Aikido - Fitness 1, Self Defense 1, Community 3, Wear and Tear 1, Instruction 3, Tradition 5, Ranking 2
Krav Maga - - Fitness 3, Self Defense 2, Community 3, Wear and Tear 2, Instruction 2, Tradition 1, Ranking 0
BJJ - Fitness 5, Self Defense 4, Community 4, Wear and Tear 5, Instruction 4, Tradition 2, Ranking 2
Tai Chi - Fitness 1, Self Defense 1, Community 2, Wear and Tear 0, Instruction 2, Tradition 3, Ranking 0
Now it's time to start playing the field. A lot of people sign up at the first place they try out. But it's hard to leave and move on to a new school once you've started and people get locked into schools that aren't always very good. So it's a great idea to try out 4-5 places before you pick one. Most schools offer a free first month of classes so you should really get the most out of this. A good way to do it is try a school for a week and figure out what you like and don't like. Do this for 5 schools and at the end, decide which school is right for you. You will likely be there for in some cases decades, so it can be a pretty big commitment.
If you're just signing up your kid to try it out, you might think this doesn't matter since they probably won't stick with it more than a year anyway. If you are going to do that, make sure you talk to the parents there, and maybe even do a background check on the instructor. You would think that because they work with kids, that guy is probably the safest nicest guy. Unfortunately, a lot of sex offenders get into martial arts instruction because grooming behaviour is very easy to establish and a lot of these schools hire guys without doing background checks. I'm not saying sensei paul is a felon, but it's so common in martial arts, that it's a good idea to take extra steps to make sure the school will be safe, especially if you don't plan to stay the entire time they are training.
Hopefully this helps you get an idea of the process you can take to find the best school to fit your needs.