I'd honestly it up a 350Z forum, there are ton of them out there and I can't believe you could not get working combos from ppl that are currently running them.
With that said, yes when you go to 18s you will need a new tire obviously since the rim is going to be bigger. Check on tirerack for your stock tire size diameter and then scroll down and see what 18" sizes meet that diameter. As far as width... that I do not know. I know on our cars running a big 10-11" wide rim is not a problem but the Nissan is a sissy girly car... I mean its a nice import sports car that might not be able to run the same widths.
2000 Mustang GT Steeda #0048 34k miles. 99 Cobra 4V swapped, FTBR IRS swapped, exhaust, tuned by James Gordon.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.