Most people who study martial arts undermine the importance of resistant training, I am not saying you absolutely must engage in strength training to become a great martial artist but it does help. Something that I hear often when martial artists bring up the topic of strength training is; ‘it will reduce my flexibility’.
That is only true if you are lifting very heavy weights and not stretching. The strength training techniques that I am suggesting are ‘explosive lifts‘ these are the type of training that Bruce Lee engaged in. It is not necessary to do a wide variety of lifts that isolate certain muscle groups.
What you want to do are compound lifts that utilize all of your major muscle groups at once for example here is a pull up routine that utilizes many different types of pull ups/chin ups as well an explosive exercise. (The clap pull up workout) The explosive moves are primarily for advanced athletes.
Bruce Lee often stressed the importance of working your core and you only need to look at a photo of him to realize that he was the type of person to practice what he preaches. The core is utilized in just about every move you do and it also keeps your back strong so if you could only work one muscle group then it should be your core;
Next most important thing to work would be your legs, here is an explosive leg workout video to start you off on;
You should also do push ups going down slowly then launching your body upwards to give your pectoral muscles explosive strength. This will help with your punches.
Most of what you need to do for martial arts can be done using body weight exercises, more advanced training can involve free weights or machines.
Another option is to do your moves whilst submerged in water, this is a technique that Donnie Yen uses to gain more strength and speed, if you don’t have access to a pool then you could opt for a weight vest or wrist and leg weights.
Resistance training will give you more power it will make you able to take more hits, it will improve your fitness, you will strengthen your tendons and make your bones more dense. There really is no reason to do it!