I recommend 17" or 18" wheels. I don't think 17' or 18' wheels would fit on any car.
Your definition of "flush" is probably different than anyone else's definition of "flush." Wheel fitment is just math. Look at your current setup, figure out how much farther out you want the wheels to sit to get the "flush" look you want, then do the math to figure out what wheel size that would be. It ain't rocket science.
If you were happy with Invos (which are really
not that great a performance tire) then you'll be happy with just about any moderately decent UHP or UHPAS tire.
You need to make up your mind on 17" or 18" if you want folks to give you more specific advice.
I'm not sure what gave you that idea, but the
RPF1s are available in a 5x100 bolt pattern in 16", 17", 18" and 19".
Fixed your link for you. Yes, their "traction pattern" is super wicked awesome. They're also a dated design - their replacement, the HTR-ZIII, has been out for 5 years or more.
I know the RS-Rs are the greatest tire in the world, able to leap tall buildings in a single bound, but I'm not sure an extreme performance tire is what he's looking for based on his budget and the fact that he was impressed by the Invos.
Or unless he wants the generally smoother ride quality that all-seasons provide (kinda like the smoother ride that a "luxury sport" tire like the Nitto Invo provides). Or unless he wants his tires to last longer than something like the gummy 595RS-Rs. Or unless he wants to spend less on tires, since all-seasons are typically cheaper than summer tires, and again, will last longer.
There's absolutely nothing wrong with any of those Enkei wheels you posted. There are more affordable wheel options out there, including used wheels, that might allow you more "bang for the buck".
You haven't found any
wheels in the classifieds, or you haven't found
undamaged wheels in the classifieds? Either way, are you sure you're looking in
the right place? 17x8" is one of the most common, popular sizes, so there are always a bunch of sets for sale.