Welcome Jackie, should you be using a slight American twang there mate? Lol, isn't it a 350zeddd, in Pomland?!
I'm running my second set of Eagle F1 GS-D3's (aggressive directionals) on my 350z, love'm to pieces, I'd put them on most cars to improve handling. I've had other flavours of tyres and keep going back again and again to the F1's (best to get hold of the German manufactured ones if you can as the composition is a bit superior to ones manufactured elsewhere). Can throw the beast around in the wet, without fear of loosing the back end, mind you track time I've done might help with that too. Everyone has their favourites and it depends on your driving style, and how hard you push your car.
Tere is the mechanical genius. I've learned a lot out of necessity & interest, but having grown up around cars and bikes helps.