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I would not recommend building a set until you have several films "under your belt" as it were. Stay in your house and your backyard. If need be, go to a local public place (like a park) when it's open and shoot there. You should not go shoot in Malls or stores unless you have permission. Definately do not shoot car chases or fight scenes in public areas without first notifying the police that you want to do so. The authorities will tell you that you need a permit that costs $50 or so. This will tempt you to shoot the car chase without them. This should not be done.
It could be a very educational experience to ask about permits for when you shoot on your block. City Planning will tell you that it costs so much money to get a permit for a day, and you will need proof of insurance (even more money) to be able to film on your own sidewalk. While this is indeed true, if you are making a small practice film with your friends and a home camera you shouldn't get into trouble as long as you don't break the law. So, use your head and your driveway (e.g. don't have your actor lay down in the middle of the road), and everything should be fine. If not, just stop filming when the police tell you too and don't come after me.
When you decide you absolutely must build a set, I would suggest that you make it out of 1x2s and 1/4" ply or composit wood. Do not use 2x4s and dry wall, not only is it really messy to work with but it also is extremely heavy. You want your sets to look solid, but be easy to set up and take down.