Just to throw my opinion in, we've had two 350s and two 370s, all have been great cars.
Started out with an 04 Ginge 350ZGT (2005-2009), loved it, wish I'd never sold it, then I got a 370Z GT Ultimate in 2009.
My wife had an '06 Roadster for a few years, then we sold it and bought a '10 370z roadster a few years ago.
In all honesty, we both prefer the 370s but they have all been great cars, and as above, if we had more space, I'd have kept the first 350Z we had.
They are GTs, but you can hustle them along and get a big grin, they're best with a few choice mods imo, or some stupid ones to give them lots more power
If you've had an MX5, the Z is bigger and porkier, but still rewarding and fun.
Enjoy whatever you choose