Cardio. Weights. HIIT/Tabata. Yoga. Pad Striking. Kihon. Musubi. Kumitachi. Shiai. Machines. Gadgets/Gizmos.
This is a topic we generally avoid because we don't want to offend those who are not "in shape" but hold high degrees of rank. We all know these people and they exist in every martial art. At some level, we resign ourselves to "nature's course" assuming that because our chosen martial art doesn't give us the conditioning results we hoped for, we are doomed to feel, look, and perform the way that we do.
Obviously this is faulty logic based on a defeated mind.
There are generally two types of martial artists when it comes to these issues: 1) Those who are overweight 2) Those who are underweight
Overweight. This is an incredibly boring segment of martial artists, not because we feel less sympathy or empathy with them, but because the answer is obvious. No matter how you do it (macros, points, etc...), the simple math is: Calories In/Calories Out. (Don't worry, we'll get to "quality of calories" later)
Underweight. This group is phenomenally more interesting because their issues generally don't reside in their carrying too much weight, but the lack of elasticity, nutrition, and overall wellness in their bodies.
Most of us don't realize that no matter what martial art you begin studying, your body doesn't acclimate automatically with your existing fitness/nutrition (or lack thereof). We get away with this when we are young because our bodies are naturally more flexible and recover faster.
Exercise is critical in supplementing your martial arts lifestyle because it keeps your body strong enough to endure the rigors of training. Much like rock climbing may really work your forearm flexors, but result in issues because of the lack of extensor work, martial arts can do the same to our bodies if studied without supplemental exercise.
So what exercise is the best? Variety is the best answer here.
Relying solely on cardio, or weights will often result in the benefits of one to the lack of the other. No striking work? You'll probably have trouble if you're a grappler and you want practicality in your martial art studies (striking, whether used as a way to damage or distract your opponent, is an important part of training).