Currently the fighting arts are undergoing a resurgence in popularity owing to the success of the UFC and Mixed Martial Arts (MMA). There is much discussion over what is the 'best' style but with so much variation in approaches from different arts from around the world, such discussion tends to be redundant and a better question to ask is what style is best for you. Even then, the quality of instruction and the rapport you enjoy with your teacher will in all likelihood contribute more to your enjoyment and advancement that the particulars of the art you study.
Ultimately how you train will depend on the art you study and the approach taken by your instructor. Broadly speaking the arts can be divided in Western and Asian martial arts. The most popular Western arts are Boxing and Wrestling, both of which have become more popular with the rise in the study of MMA. The most popular Asian arts are Chinese (Kung Fu), Japanese (Karate and Judo) and Korean (TaeKwonDo) but you can find online guides to the history, philosophy and technique of many more diverse methods on this site.
Train Hard, Live Easy!