is there anywhere I can find a list of all martial arts?
There wouldn't be a compreshensive one, anywhere really. Why? Too many hybrid styles that are taught by only one instructor.
Martial arts tend to fall into a few categories: 1) does it make you a lethal weapon? Every one of them except Aikido, because of it's defensive nature. 2) Does it involve grappling primarily, or punching & kicking? karate, tai kwon do, and many forms of Kung Fu all involve punching & kicking. Ju jitsu, hapkido, and ninjitsu more of the grappling variety. 3) is it circular or linear? Kung Fu is more circular, and Karate is more linear. 4) Is it "traditional" or a mix? Kenpo karate is a mix or eclectic style of karate. However, Shotokan is traditional. By doing some research on the specific name of the style, you can find it's lineage, which then can tell you about what tradition it has & whether or not it may be right for you. 5) is it considered defensive or purely exercise? Most martial arts are partially a form of self defense. However, Tai Chi is largely a form of exercise.
Given that any city will only teach a handful of styles of martial arts, it would be best to find out what gyms teach what forms of martial arts locally, because you need a master, in a gym, to teach you proper technique, which can't be learned online or in video.
Then, once you've checked out a few gyms, you'll know both the style of the art you want, and the instructor.
Here is a link for you to check out about all things martial arts: