I seem to have an unusual position on what kind of trunk exercises are appropriate for combat sports. Most trunk exercises I see done are bodyweight and done with a large numbers of repetitions or simply isometric holds. While this is as good a way as any to do conditioning, I don't see it as benefiting the needs of a fighter very much.
In striking and weapon arts the primary ways in which the trunk muscles are going to be used can be divided into offensive and defensive. On the defense I might pull my head backwards quickly, arching my back as I do, so that I can dodge a strike; or duck to the side turning my torso and basically doing an oblique crunch while standing. On the attack my trunk is used to transmit force from my legs and hips to my upper body to make for more powerful hits.
Each of these applications have several important characteristics in common. The movement is sudden: it does not build gradually, it must be made in an instant; the movement is fast; and the movement is high intensity: that is rapid acceleration (and then deceleration).
To this end our trunk exercises should be geared towards producing sudden, fast, high intensity movements. We don't do that with exercises that are way out on the endurance end of intensity. Nor do we do it with isometric exercises.
I suggest four categories of trunk exercises for the fighter.
Conventional Strength Training - Exercises like weighted crunches, obliques, side bends and hyperextensions. The important part is to use enough weight that you can do only 8-12 reps max. Higher intensity i.e. 6RM or less, is not recommended for small muscles like those of the trunk nor for single joint exercises, which these effectively are. Lower intensity builds more strength than endurance and for our purposes we need strength.
For someone who is brand new, isometric exercises, like planks and bridges, can be a reasonable starting point, but only until a 30 sec. hold is possible. Then you need to move up to dynamic exercises. And if necessary start doing crunches and the like with no weight, but only until you can do more than 12, then you need to add weight.
I actually see machines as a perfectly good way to do these exercises. Things like an ab crunch machine, back extension machine or torso rotation machine. But I say that in the context of a person doing a program that includes four different kinds of torso training as well as their technical training. The advantage of a machine in this context is that it allows for higher weights, which builds more strength and power. And I wouldn't do machines all the time, I'd do them in the run up to a competition when I'm looking for max strength and power in my entire program.
Structural Loading - Structural loading is the demand on your torso muscles from lifting and carrying heavy weights. While doing exercises like squats, deadlifts, lunges and step-ups* you have to stabilize your torso against the weight. The higher up the weight is held the greater the demand on trunk muscles, so racking weights at shoulder level in the clean position is more challenging than having dumbbells hanging down by your side.
For single leg exercises it's beneficial to hold the weight on the opposite side, such as doing right leg step-ups with a dumbbell in the left hand and vice-versa.
A variety of different exercises will provide a variety of different challenges to your trunk muscles allowing for some fairly complete training of the torso.
* This list isn't exclusive, these are categories of exercises with lot's of potential for variation. Additionally, a wide variety of non-conventional weightlifting options exist which will fulfill this objective. Examples include: sled drag/push, tire flipping, side presses and lots of other options.
Plyometrics - As the needs of our torso muscles are primarily these are important exercises for the program. The neurologic component of any plyometric exercise is driven by the reflex traveling from the muscle to the spine and back. For trunk muscles this is necessarily shorter than any other joint. As such it is most important with trunk plyometrics to minimize the contact time.
Suggested Exercises: Floor slams, Back throws, side throws, reverse/back side throws. As well as chest pass/bounce with a hip pivot.
High-Intensity Trunk Conditioning - There are several options for High-Intensity Interval Training that will also provide a valuable training load on the trunk muscles that stabilize your torso. Battle ropes, clubbells, sledgehammer and similar exercises.
My preference is for heavy bar cutting patterns. Taking a 9+ lb. exercise bar doing cutting patterns is a good high intensity exercises for intervals. Plus throwing around that weight at the end will challenge all of your balance muscles from the ankles to your upper back. This can be put together by buying a 4 foot iron pipe at a home improvement store, and then filling it with sand. The result is cheaper than a sledge hammer (or clubbell) but with similar characteristics.