Is there any Hadith that discusses the importance of exercise, its benefits and what kind of exercise is considered good, etc.?
According to the fatwa here, muslims should be strong physically and mentally.
Personally, I think those exercises which just make your biceps big are stupid exercises, you need exercises which will give you overall body strength, core stability, flexibility, agility, and stamina.
I used to work with someone who was a professional bodybuilder, and he said when it's competition time, his water intake has to be so precise to give him the perfect definition that he kept getting full body cramps due to the lack of water.
What use is such a body if you can't move properly? So personally, I would recommend staying away from that type of thing, and finding an exercise which will give you strength, core stability, flexibility, agility, and stamina.
The only exercises I can think of which does all these together are the gymnastic exercises. Please note, I am not suggesting you become a professional gymnast. What I am saying is that gymnasts do certain exercises which give them amazing strength, core stability, flexibility, agility, and stamina all at the same time! What I am suggesting is that you find out what they do and do that. Plus find a decent martial arts system not concerned about competitions and belts.
Just keep these words in mind, fundamentals and conditioning.