They actually handle quite well. The Z is and always has been more of a track and cornering car than a balls to the wall 1/4 mile burner.
You can pick up a 350Z for a really good price, but if you have the money, I’d say get a 370Z and be done with it. They’re shorter, lighter, and more powerful. I figure if you’re looking at an M3, you can afford a new or slightly used 370Z anyhow.