For my first car coming out of college, I needed my parents to cosign, otherwise I wasn't even going to get financing, let alone a halfway decent interest rate.
Fast forward over 10 years, and I have a better job and credit position such that I can get something on my own.
You should get the car you want, and a Z will likely make you very happy. But don't bend over backwards to make your first car a Z if it locks the rest of your life up with little extra spending money. You may actually come to resent the car for it. Just a little warning.
Don't forget to check out insurance rates, annual registration costs, gas costs (estimated), and regular maintenance costs (~$80/oil change alone?).
A new car at your age might be an awesome thing to do, but it also might be the worst mistake you could make, financially. So I applaud the questions and caution. And please drive with care.
Ruin your car in 2 years, and you're basically bent over for the next 10, with nothing to show for it. This is why powerful, sporty cars are not for every young adult, and why insurance rates are crazy.
And nothing beats just going into a bank/credit union and asking to talk to someone. If you don't feel like they're going to help you out much, look at another one. It's in their best interest to put you in the best possible position for success.