The 315/30 18 is the largest tire currently available for the stock rear wheels of your Z06. Others here have done away or modified their rear brake vent in order to fit a 335 on the rear. I tried some on one time & they certainly look great but I didn't go that route as I want to avoid brake "fading" due to lost heat dissipation. I would hate for that to happen when I really needed to stop!
Personally, I prefer the Michelin Pilot Sport IIs (aka PSIIs). They have great treadwear, temperature, and water management ratings. They're one of the more expensive tires for your Z, but I think they are the best all around choice. I live in Denver and the rain can play havoc with the stock F1SCs. When someone makes a 315/35 or 40, I'll be all over them as most of the available selection doesn't fill the wheel well as much as I'd like. There are some Nitto "riders" here as well that can give you their experiences as well.
*laughing* It's amazing how often this question arises. I asked it only 2 months ago and have seen it asked multiple times since.
"Was it over when the Germans bombed Pearl Harbor?! HELL NO!" -Bluto
2002 Torch Red Z06 - Stock