Your first week behind the wheel, and your DIY chops, will likely dictate your first project.
For me, it was a swap of the factory audio head-unit, followed by sound-deadening the trunk.
Exhaust work is way out of my league, but I'm currently working towards replacing the anemic-sounding stock exhaust.
So far, I find the Z has more than enough power to keep me entertained, so upping torque is something I will likely leave until much later, if ever.
As has been said, it's all about your personal priorities.