Martial arts vary on country of origin and fighting philosophy. They ALL have something to offer, otherwise they would have died out years ago. Anyone who claims their style is "the best," needs to explain "at what," because they all have advantages and disadvantages depending on the situation. Since there are so many styles, they can be categorized in many ways in order to highlight the differences. First, martial arts can be distinguished by the overall methodology, of which there are three basic categories: pugilism, grappling, and wrestling.
Pugilism is boxing, but may also include kicking. It is useful for addressing multiple opponents simultaneously by keeping them "at arm's length" during the encounter. Karate is an excellent example. There are several styles, but the basic four of the World Karate Federation (WKF) are Shotokan, Shito-Ryu, Goju-Ryu, and Wado Ryu. All are very balanced, spending equal time on both hand and leg techiques. Karate is considered Japanese in origin (Okinawa).
Tae Kwon Do is similar, but emphasizes kicking much more than punching. It is also Korean in origin. Since legs are longer and stronger than arms, practitioners believe they can keep opponents at a greater distance and deliver more powerful techniques. Should this be the discipline of choice, keep in mind that developing leg flexibility and strength takes about a decade before the reflexes have developed to combat-worthy proficiency. Hand attacks are much faster in a conflict and easier to train.
Grappling involves blocking an attack and "binding" up the opponent, taking them to the ground for wrestling. Grappling was designed to take down a pugilist and "tie him up" until he chokes out or submits. It is not good for multiple opponents. (Taking one opponent down is great, but then the others have 'open season' to attack.) Judo and Aikido are great examples of grappling. Both are Japanese. Be prepared to learn how to fall... again, and again, and again.
Wresting is superior for the strong, one-on-one ground fight. It requires strength and stamina. Greco-Roman wrestling is the prime example. Again, not good for multiple opponents. Smaller frame individuals will have a serious disadvantage in this art.
Most martial arts are pugilistic because it is safer to stay on your feet and doing so allows one to address multiple threats.
Martial arts can also be divided into hard and soft styles. Hard styles are very physical, emphasizing clenched muscles on impact. Soft styles are more about internal harmony and personal health-focusing on relaxation and coordination.
Kung-fu is a Chinese, pugilistic, hard style. Tai chi and qi (chi) kung are soft styles. Tai chi is low impact and performed slowly, making it ideal for the elderly. Although martial applications may be derived from the movements, this is generally not the intent behind practice.
Martial arts differ a great deal on philosophy. What is the best way to be victorious in every conflict? Pencak silat and other Indonesian martial arts believe in attacking the weapon. Ergo, if an opponent punches, the defense is to strike the arm and render it useless. The same can be said for a kick.
Most martial arts are based in self-defense. One exception is ninjitsu. Ninjas were hired assassins in Japan. Ninja training involves knowledge of penetrating castle defenses and stealthy attack-retreat training. For this reason, Ninjitsu is not recommended for children.
Since Bruce Lee grandfathered Jeet Kune Do, and especially since the advent of the Ultimate Fighting Championship (UFC), the recent trend is toward Mixed Martial Arts (MMA). In other words, the student is encouraged to take an eclectic tour through the martial arts, "stealing" the best that each has to offer until ultimately the perfect style develops for that individual. This is how a new style is born. Unfortunately, this is unwise for beginners. Beginners need the structure and discipline of one martial art until mastery occurs, otherwise ineptitude and confusion will ensue. Krav Maga is one example of a MMA from Israel and encompasses pugilism, grappling, and wrestling.
The most important element is a good instructor. Too many instructors open up a dojo and have the pressure of a huge overhead looming over them. This pressure often leads to premature belt promotions so that students think they are improving rapidly and decide to continue training. Percieved success and growth entices the students to stay. It is not the belt that determines success in combat, so it is wise to be suspicious of black belts given out in less that 5 years. Contracts guaranteeing a black belt in less than 5 years should be a HUGE red flag.
In this author's opinion, karate is the best place to start. Karate is practical, balanced, and beautiful in its simplicity. Like any art, practice and time will bring mastery. Karate allows vast self-defense possibilities as well as wholesome family time. Once basic mastery is achieved (first degree blackbelt), it can be complimented by one of the other martial arts noted above based on the interest of the student.