Congratulations!
Some quick thoughts:
Road noise - I've had notable success dampening road noise with a layer of GTMat (non-brand name Dynamat) and generic closed cell foam (CCF) from Amazon in the trunk floor and double layers of both on the rear wheel wells. Multiple threads here on how to accomplish that.
Engine noise, lack of - Z1 cold air intakes really let the engine sing. Round out the symphony with a Fast Intentions exhaust and some high-flow catalytics.
Now for the real fun part: you have a 6MT, which means you have a CSC. Which is going to fail. Repeatedly. Replacement requires dropping the transmission. So unless you intend on putting your local mechanic's kids through college, invest in a CMAK from ZSpeed. Trans only has to come off once, and while it's off you might as well get a new clutch and flywheel. Package deal for all that runs about $1,300. And if you do intend on putting your local mechanic's kids through college, there are ways to do that with pre-tax dollars
Additionally, I've heard Miami is hot. Temperature-wise. The 370Z is undercooled, and will start pulling timing once oil temp hits 240*F. I'd recommend a Z1 Motorsports 34 row Setrab oil cooler kit. Pretty much every mother's son on here has installed an aftermarket oil cooler, and the ones who say they haven't are probably Russian bots.
Again, congrats! Feel free to PM me if you have additional questions.