Finding a dojo or style that fits you can be a bit of work. But essentialyl here is my advice:
1) Get a general idea of what martial art suits your body type best and which one interests you most. Ideally these two attributes are the same martial art. It sounds like you are really interested in karate but I would advise just learning about other styles before making a final decision. If you're not into the grappling martial arts (like judo or brazilian jiu-jitsu) you might want to check out muay thai kickboxing or perhaps wing chun, as these are more striking based like karate and may suit your reach advantage.
2) Go through the phone book, or maybe even a website that may list your local dojos. Call the ones you are interested in and ask if you can come by and observe a class. Many dojos will even offer one free class so you can get a feel for the instructors. They'll tell you what to wear, but you shouldn't need any equipment since you most likely won't be sparring the first day. It's very important that you go to multiple schools and not sign up for classes at the first school you go to. If you indeed decide on karate and visit multiple schools, you'll notice that there's a tremendous variation among the styles of karate. Like you said, there's some karate schools out there who primarily market themselves towards children. However there ARE karate schools out there that are pretty hardcore as well.
I hope that helps. If you have any other questions feel free to ask.
