Fighting vs. Martial Arts
First off, let me approach this from a different direction; what we see in movies and on TV is dance. It's a choreographed series of movements to display an idea of fighting, not actual combative action.
The martial arts are codified systems to train a person to fight. In modern times, more spiritual and psychological meaning has been attached to them, but underneath, they are about learning to fight efficiently and have evolved (hopefully) with experience of those who took the art into the world and survived to say what worked.
At the base of the art is the ability to fight. You can learn this on your own (or rather, without an instructor), but you will be learning the meaning of the "school of hard knocks". Monkeys can kick and scratch and bite and strike. Padding up and beating the crap out of some friends can teach you to pack some power behind your strikes. But this is not a codified system of fighting, and while you may emulate the movements you think you understand, you will be wrong.
Learning Martial Arts
The beauty of martial arts is that someone long ago started the journey for you. Even Krav Maga's Imi Lichtenfeld took the fight from the slums of Hungary before it became what it is today. But if you were to do what he did, you would not be learning Krav Maga, but your own style of fighting.
Martial arts can only be adequately taught as effective styles by those who understand the styles. Understanding the styles means training in the style with someone who understood it before them. It's passed down from teacher to student, imparted with the fine tuning that has come from generations of teaching. Training at home will not give you this adjustment.
Beginner Instruction in Martial Arts
Most schools advertise with children, because this is their bread and butter. Kids see TV shows and "want to learn to do that". Parents want to make their children happy, so they enroll them in kids classes.
Most every instructor I know has loathed teaching kids classes. It's an hour of babysitting for parents who want to do something other than listen to their kids complain. However, it pays the bills.
During the evening, most of these schools offer adult classes. These are classes where the real art gets explored. There aren't any children, and in good schools it's a good chance for adults to get out some aggression in a healthy setting. Calling schools to find out about their adult programs will give you a better start.