Most setups will have a 30-40mm stagger from front to rear. Not all brands and models of tires have the same sizes available, so you just have to sort of pick from what you're provided with. Personally, I would start with the type of tire usage (ie: all season, summer, high performance summer), then look through the proven choices in that segment, and then try the sizes available. Most manufacturers have a pretty good selection of wide 19" tires by now, unlike the market for 20" GTR tires.
Here's one example for maximum summer grip that serves many members here well:
Bridgestone RE-11
Front: 265/35-19
Rear: 305/30-19
The guys running these same type of wheels on their 350Zs and G35 coupes are used to tire sizes like 245/275 and 255/285, but the 370Z can just fit a much wider tire setup. I would personally suggest either 255/265 in front and 295/305 in the rear, as previously mentioned here. Brands and tire models are more of a personal preference than anything, so I would definitely start with the intended usage first and then consider sizes from there.
Tire Rack's website may not have the specific advice you're looking for, but it can at least give you an overview for what sizes are available, whether or not a certain tire is more all-season or summer-only, and what some general opinions of them sounds like.
Feel free to shoot me a PM or give me a call if you want to discuss further. Thanks for the vouch!
