if want to improve your speed, first you need to have strong motor (your muscle) so that you can do the acceleration.

Velocity (v) and acceleration (a) is totally different thing. To have more explosive move, you need to have more explosive muscle to do the explosion. just apply the physic into it;

a=v/t, (t=time)
F=ma, (m=mass, F=force)

That's why sprinter will always have bigger muscle than marathon runner. So that they can run faster.

To be honest with you, if you want to be fit and healthy, you must at first to join the bodybuilding. Because fit and healthy is part of the bodybuilding, you need to have the knowledge of bodybuiling to know what fit and healthy is. It is like you say you want to know how to jump without knowing the rest, but you dont even know how to run at the first place, then how you want to jump?

Bodybuilding is a very wide range of body knowledge. It is almost same as human anatomy study. It is not only about carry heavy weight, and eat anything that in front of you. You need to know how to do it correctly, what to eat correctly. And it is not easy to grow lean and big without proper knowledge, and you dont hope you can grow big or fit or healthy just by eating pure protein everyday. World dont go around that easily without any other factors and variables.

It is ok to set your goal as you want to be fit and healthy. But also dont because of that goal and you neglect other knowledge and it might limit yourself to your goal. Who knows you might end up changing your mindset and your goal.

My meaning of bodybuilding is not totally on weightlifting, it also consist of the understanding of bodybuilding like what is the body metabolism, protein that needed for the body and a lot more. If want healthy and do exercise only, i dont think that's enough for these days especially the outside food or the ingredient that you get from it. A lot of people think they are living healthily like their day-all-meal eat or drink fruit juice, some i even heard of they say they are healthy because they have plain roti canai for their meal. From which i think they dont really understand how exactly the body support to work. For me, the bodybuilder is the world most concern about their body's person, they can really fully understood their body and how it suppose to work. But of course not all bodybuilders are the same. Some just simply do powertraining, bulking or a lot more.

This is just my 2 cent.