Many martial arts are quite structured and have governing bodies and federations which you can contact for advice about reputable dojos or sports clubs in your area.
I remember when I started karate class as a kid, I thought it was kind of cool that I had to apply for a "license" before I could train. I used to joke about it being my license to kill, using my lethal karate skills. Of course I would only ever use martial arts for self defense...but I was like 10, so cut me some slack! :)
As for the benefits, there are some obvious health ones, and you'll be surprised how useful it is to build up core strength, flexibility and balance in your daily life.
But I felt like going to karate class was a cool way to socialize. It was also kind of relaxing, repeating katas and being focused means your mind doesn't have time to worry about all the other things going on in your world.
Then there's the self-discipline and confidence perks...the benefits of martial arts are seemingly endless!