In Choosing a School, I stated that the instructor may be the single most important of the variables in choosing a school, and the quality of the Students is a reflection on the teacher. But they are not the only factors. Here is some information on what to expect from different cultures and arts. This information can help you choose a "style" as well, and maybe give you a starting point.
Choosing an Style
You should decide what you are looking to get out of the Martial Arts, and do not be afraid to ask the instructor about those points. There are Sport Arts (Judo, Tae Kwon Do, Tournament Karate), Striking Arts (Karate, Chinese Boxing, Tae Kwon Do), Grappling Arts (Aikido, Jujutsu, Ch'in Na) and Weapon Arts (Kyudo, Kendo, Escrima). Arts have different philosophies and goals, you need to pry a little to learn what those are. You should decide which one interests you, and then look into the schools that teach that style, in your area.
Cultures effect the arts, so we look at "Style" and origin of an art to see what its influences and philosophies are likely to be. Many arts are effected by the culture they are taught in, and the beleifs of the instructors. So if you get an American Instructor there is a good chance that he will teach a more Americanized version than an instructor from somewhere else. This can be good or bad depending on what you are trying to get out of the Art. It is easier for people to understand people of their own cultures -- but if you are trying to get the other culture out of the art, then you should make sure that the instructor knows that culture well.
Here are some rough over-generalizations for what to expect from Cultures and their influences
The Chinese arts are the most difficult to classify because China is the largest of the countries, and has great varieties of people, climates, terrain, philosophies, and so on. About the most consistant thing in chinese arts is that the Chinese are a people who value their mystacism and secrets. But we can break the Chinese arts into some sub-catagories to understand them better.
Because of the Mystacism in the Chinese Culture, they tended to do things like observe nature, and try to harness the power of nature, by mimicing movements (force) in their arts. So many Chinese Arts have an influence of some Animals (or nature) in their name and in the motions.
Japanese / Okinawan Schools
Japanese Arts in general tend to be very disciplined and formal. If you are looking for a "laid back" class, with a relaxed atmosphere, this is probably not it. These classes tend to be structured to ritualism. The Okinawans don't always appreciate being grouped with the Japanese -- but stylistically, they had a lot of influence on many Japanese Arts, and this is reflected in the similarity between the styles.
Japanese schools have "hard" and "soft" (external or internal) arts, like the Chinese. But the breakdown is sometimes hard to fathom, and less clear. Often the weapon arts, and most schools of Aikido, tend towards "soft" (internal) -- and in fact permeate the art with the philosophy. But even many of the "hard" styles (like Shotokan) work on the philosophy as well (in a slightly different way).
In Japanese schools it is sometimes important to know whether a school teaches a -DO art or a -JUTSU art. Since this is usually a suffix on the art taught, this is not difficult to find out (examples: Aiki-DO or Aiki-JUTSU, Ju-DO or Ju-JUTSU).
In their own catagory are the Weaponed Arts. They are usually DO arts (KyuDo, KenDo), but not always. 'DO' schools teach self discipline, patience and philosophy, by learning a particular (archane) weapon. Their application in self defense, in modern society, is limited; but the philosophy and character learned in class, can be applied through out ones life.
Korean Arts in general work on high kicks, spinning techniques, and usually require some "breaking" (destruction of wood or bricks). Their classes are usually very disciplined (lightly militant). There is usually a lot of sparring in Korean Schools. They are favored among competitor types, people that want to go to tournaments (and win), or people that want to be able to "show" what they have got. For children these arts are usually really good for discipline and for "bringing out" shy kids (self confidence).
Tae Kwon Do, Hwa Rang Do, Tang Soo Do, Kuk Sool all tend to work on the more flashy parts of the arts (relative to other martial arts). They work on power, discipline and competition. These are striking arts, but most also teach some grappling techniques.
One of the hardest things in the martial arts to control is ones own ego. Competitive arts (like most Korean Arts) tend to do the worst job at this because they are have to inflate the ego enough that the student makes a good competitor. I have met many excellent Martial Artist from Korean (and other competition oriented schools), but sadly I have also met the worst from them as well. There is a balance that must be maintained and weighted at all times. Competition and Korean schools are perfect for some kids (and Adults), but it can also be like throwing Gasoline on a fire.
But for every rule in life their seems to be an exception. And some Korean schools don't fit the stereotype. Some HapKiDo schools can be far more like an Aikido Class (where the art derived from) than another Korean school.
Escrima, Arnis and Kali are becoming more common. These arts are generally taught in a relaxed atmosphere, with an emphasis on drills. The majority of the time in class, will be spent practicing with a partner using stick(s) or empty hands. Knives (wood or dulled) will probably be added later. Sparring empty handed and with sticks or other weapons may also be taught. These arts are useful for close in fighting with empty hands, and they also work well against opponents with sticks or knives.
The classes are usually extremely informal, and if you are striving for external discipline these schools are unlikely to meet your needs. Because of the more casual nature, there is often not as much seperation between ranks -- and it may be more possible to make "friends", even being more friendly with the instructor (in other arts a student must be far more aware of his place). Even though these arts are based around weapons, they are amazingly practical in the modern world (far more than say archery or a long sword).
This is deceiving, there are no "true" American Arts, other than ones practiced by the American Indians. However Americans are known for putting their stamp on things, and the Martial Arts is no exception. If you or your child is studying with an American, he is probably putting an American influence on the art or in the way he teaches. It is easier to understand commands called out in our native tongue, and understand moves given americanized names. If you or your child are American (or Americanized) this might aid in your learning. If you have a real tough time understanding an instructor or his teaching methods, you might want to find one you are more compatible with. Understanding what is being taught is probably more important than the cultural loss.
Traditionalist argue that the arts are products of a country and should retain that countries names for everything. I agree that a little added culture can't hurt, but it doesn't make a significant difference either. MacDonalds in Japan renames items on the menu (Bigu Maku) and this does not detract from the experience of eating a burger.
There are good and bad Instructors from everywhere.
Choosing a System
Remember it is you (the student) that will dictate what you are to become, not the art; "it is the artist more than the art itself". Only you can choose what is best for you. If however you are looking for a self defense system, and you are a person in relatively good health, here are some guidelines to follow when choosing to study.
I prefer students to practice something that is easy in the beginning, that they can learn and use to defend themselves quickly. This instills confidence in their abilities, and backs up that confidence with some ability. Later, as the student progresses he can be challenged to learn more complex systems and movements.
The closer in to an opponent you get, the faster things will move. This is the same principle that causes liquids, gases and solids to get hotter (more excited, at the molecular level) as they are put under pressure (closer together). Applying this principle to people, the more distance between two fighters, the slower the fight. Since the beginner needs time to react, the slower (longer) the art, the easier to learn. Realize that most arts overlap, and they work at multiple ranges and techniques, but on the whole they can be roughly categorized.
People are dynamic (ever changing), and as your wants and needs change, so will your interest in different arts. Don't be afraid to try something new! But don't get flighty because the grass looks greener in some other pasture. Balance is the key. However, if you are not getting what you need out of the Martial Arts, then perhaps it is time you tried a different Martial Art. (Eventhough many instructors will try to convince you that this is not good).
The following are modifiers or qualifiers for different schools. Some arts do more than one of the following, but they all have to put a focus somewhere -- as do you. Here are some modifiers:
Long range arts tend to be the easiest to learn (Karate, Tae Kwon Do, Northern Kung Fu's etc.). These arts tend to defend themselves at long range (kicking and striking). Since the distance is further away, a student has more time to react, and he can learn how to see attacks and read them. These distance arts also tend to teach maximizing power. (Overcome power with power.)
Short range arts -- Southern Kung Fu's (Wing Chun, etc.), Filipino Arts, Kempo, etc. These arts often require a great degree of proficiency before a student is capable of defending himself. As the range closes the speed increases. Also because of the shorter reaction time, students are required to learn more complex moves; blocking, striking and leg checking simultaneously. This added complexity can make the advanced practitioner of these arts more capable of defending himself in the long run, but the trade-off is the time required to reach this level of proficiency. These arts tend to teach maximizing speed. (Overcome power with speed.)
The closest range arts are the grappling arts (Aikido, Judo, Jujutsu, etc.). These art are very close range, and that causes danger. It also requires a high degree of proficiency before it is truly useful against a fast bludgeoning attack, or dirty tactics (eye pokes, bites, etc.). These arts are very useful, almost immediately, against many types of grabbing or holding attacks but sometimes less so against a fist fight. These arts tend to teach maximizing technique. (Overcome power with proper technique.)
The specialty art may teach a sport/competition (Tae Kwon Do, Judo, Boxing), it may teach a weapon (Kyudo, Kenjutsu, Escrima), or it may be a form of exercise and meditation (yoga, Tai Chi Ch'uan). If you are going into one of these arts, realize that you are specializing. Understand what you are, and are not ,going to get out of that particular art -- and if you are benefiting (which you are almost garanteed to do), then by all means do it!
There are no shortcuts to chosing the right school or art. Every instructor beleives his Art is the best -- if he didn't beleive so, he would not have put decades of effort into becoming an instructor of that art. The students of those schools are also being programmed with the schools dogma. This is not as bad or as harsh as it might sound -- it is just a form of enthusiasm.
The Martial Arts are good for most people. I recommend them for almost everyone. But take your time, and choose the right school -- that will greatly effect your experiences with the martial arts in general, and probably define how long that you stick with it.