[carmencx3]

What is the widest tire I can put on my 18 inch factory rims or what size rims do I need to make the tire stick out flush with the body

 

[PandaG]

What is the widest tire I can put on my 18 inch factory rims or what size rims do I need to make the tire stick out flush with the body

I think 245 is the widest. My summers are on 19's though (245/40R19). It gets them nice and flush with the fenders. See my garage pics for reference.
Just note that you'll be shaving a bit of gas mileage off though. Not huge but it's noticeable.
Plus those little tiny bumps on the rear of the fenders are rendered useless I'd guess