I just picked up some 18X8.5 for the front and 18X9.5 for the rear with the factory wheels being 18X8s and 18X8.5s.

Am I going to have any problem mounting the stock factory tires (225s F and 245s R) on the new wheels?

I guess the rims might stick out from the side-walls a bit...

I am not adverse to picking up new tires but that will kill my budget for the race tires...

 

NISMO recommendations for their wheels (same size as yours):

# Use only the recommended tire size, P245/40R18 (18 x 8.5 wheel) or P275/40R18 (18 x 9.5 wheel).

The tires that you stated may fit, but I would not feel safe.