Don't do any performance mods until you get used to the car. If your dad drives the car he WILL notice gears. That is not a mod that can go under the radar. A shifter is great and something you can do yourself and with dad. I have done my exhaust and aluminum driveshaft on my car with dad (I'm 38 he's 64) and we put a B&M shifter in his Vette. Exhaust, shifter, springs and such are good mods that will let you work on the car without getting into trouble. Get your dad involved in helping with the car. The more you include him the more likely he will let you do other perfomance things in the near future. On the road, resist the temptation to keep your foot in the gas. Never, ever do anything stupid in a heavy traffic area or surface streets. Just too risky with the police or getting someone hurt.
As for having a fast car at a young age, I had a 78 Cobra II as my first car when I was a senior in high school. I never got into any trouble until I started college and then used to get tickets every month and a half. Had to pay for them myself so it gets expensive to play. Congrats on the car and have fun with it.