$8k - $13k is your price range? That doesn't give you a ton of options for picking up a used Speed3. I did a quick search on cars.com and with a max of $13k everything has 80k+ miles. As long as you get one that has the basic maintenance done.. brakes, rear shocks replaced, fresh fluids (brake, transmission, regular oil changes), and there doesn't appear to be any major damage or issues you should be OK.
Another thing you can do is read about the smoking turbo problem some of these cars have and figure out how to check the car out to see if it has that problem.
As far as the Mazda3 vs MS3 debate... I would agree that since you're 17 a Mazda3 would be a much better buy for you given your budget. Insurance will be cheaper, it will be plenty fast for you, and you'll be able to get a lower mileage and/or newer example with your budget.
Welcome to the forum and good luck with your new car search!