Are you earning this car with your own money or is someone buying it for you?
Age doesn't matter so much as maturity, responsible driving, and being able to be take care of oneself. Neither age nor the car make the person.
I personally find no reason to pick 350z over a 370z if you can afford it. However, I will just say that most 17 year olds I know have horrible habits, skyhigh insurance, poor job(s), poor career, and need to protect their personal debt before they're in big trouble before even 21. Make sure the important things in life are being taken care of before the expensive toys.
Also, the Z looks great, but performance-wise is starting to show it's age. Just keep that in mind as well! (Then again, performance-wise, it's not like you can hit 8/10s of the Z on public roads anyway.)