Well, there are two forms for running.
The "older" form is landing on your heel, rolling to the ball of your foot and pushing off there.
The "newer" form is you land mid-foot and push off from there. I'm sure the ball of the foot is fine too, but a coach of some sort might argue this.
The idea of why you do not land on your heel is this... it's like you are putting the breaks on when you heel hits the ground. BAM! Hit the ground with the heel... then roll off. And when you think about it, it makes sense.
The idea of landing mid-foot is that you are not putting on the breaks... and you focus on high cadence to speed up... not stretching out your legs to speed up. This is how we all learn to run though... to speed up you stretch out your stride. The "new" form says this is not a good.
I would NOT watch other people run to learn how to run. Most people just go run and don't think twice about what they are doing or their form.
I went to a running coach for 6 months to learn how to run. To change my form from a heel strike to a mid-foot plant.
As for your shoes, get shoes that are made for you to run in. This will prevent injury from occurring. Go to a store that specializes in running and running shoes and have them help you pick a shoe that works for your stride.
Good luck and keep at it!
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"