I would suggest deciding on the tires first.
For example, for BFGoodrich g-Force R1 the recommended rim width for 225 wide tires is 8 inches (I sent them a mail).
For Kumho v70a the recommended rim width for 225 wide tires is 7.5 inches for 17 inch wheels and 8 inches for 18 inch wheels.
Anyway, as a general idea, I would go with a width of 7,5 inches at a minimum for 18 inch wheels.