Great choice of cars! You will love it! I added a Fast Intentions CAT back exhaust and cold air intake system to mine. She is now wicked fast, but that is how I like her. These upgrades are a bit pricey but really change the performance of the car.
There are some other subtle things you can add like replacing the black plug just below the license plate frame with a back up light (see link to pic below). This black plug is a fog light in Canada, but in the US the older Zs have a blank plug in them. I believe the 2014's actually now have the light in lieu of the black plug. All of these things require some mechanical expertise or professional installation. The accessories for the Z are pretty extensive! Enjoy!
Here is a link to the back up light that I was referring to above, it cost about $60 not including installation. Really adds impact to the back of your vehicle. If you are handy or you have someone who is handy available, the install took about an hour.
http://i.ytimg.com/vi/eAl4dHQWE6M/hqdefault.jpg
Another Rear Fog Light Install...