Part of finding the right school also means finding a style of martial art you enjoy.
Striking or Grappling?
There are arts that teach striking, which is punching, kicking, etc. And there are arts that teach grappling, which involves throws, ground-fighting, etc. In my experience, people tend to gravitate towards one or the other. However, that is changing with the popularity of MMA. Does punching a bag sound like fun? Or would you rather learn how to throw someone to the ground? Figuring out if you're a striker or a grappler is the first step.
How Competitive are You?
Some people thrive on competition. They want to get their moves to work on a fully resisting opponent. Others are looking for personal growth and development, and don't really care about besting someone on the mat. Different arts will have varying views on competition. For example, Aikido is non-competitive. Techniques are practiced and perfected, but generally the art is more about personal development. Judo, which is also a grappling art, is extremely competitive and has matches worked into almost every class. Other arts like Jiu-Jitsu and Karate have a little bit of both. Deciding what your goals are with the art will also guide you to the right program.
How Much Punishment is Acceptable?
Martial arts are a contact sport. Other humans will be trying to punch you, choke you, and/or put you in various contorted positions. You'll get pinched and bruised. Your muscles will be sore the next day. However, the amount of physical punishment varies greatly.
Keep in mind, much of this also depends on the instructors. There are also people who opt out of the combative part of class. Even in full contact karate, you can participate in everything except fighting. You'll work up a sweat, perfect your kata, but pass on the actual combat. People also do this in BJJ and Judo. As long as the instructors are fine with it, you shouldn't have a problem.
Take some time to try out different arts and programs. This is one of the reasons why we have so many at our school! Different people will gravitate towards different kinds of styles and training. Never feel rushed to settle on one style. You'll be happier long term if you find a martial art that fits with your personality and preferences.