You'll find 17 in wheels are substantially lighter.

Wheel gap is not affected by wheel size as it is the tire that matters. If you fit the correct size tire then wheel size will not affect that gap.

The look is different with larger wheels because the light colour of the wheel draws your eye away from the black tire. Fit dark rims though and you'll not notice them as much.

Wider rims do appear to fill the wheel wells more but also are heavier. Using non stock offset can also give the appearance of less gap but be careful with this option as offset affects steering and handling. Using less offset can cause poor handling.

Fitting wider lower profile tires on larger rims does not affect traction. Grip levels remain much the same because grip depends on tire compound more than anything else. Tire profile affects cornering behaviour but not traction. If you've got more power you need a bit more understeer to allow the chassis to put the power down.

TRD fits 245/40x18 tires to its optional TRD GT86 model sold in the UK but on 7.5x18 wheels. Reports are that this reduces understeer (since understeer isn't really a problem with this car, this is not an advantage) and improves handling but its hard to say if this results purely from the outstanding Michelin Supersport tires rather than the plus one sizing.

The lesson from this is wider rims and tires may not improve handling. Generally, you'll have more fun sticking with 17x7.5 wheels and fitting those stickier summer tires than going up one size. Handling over bumps will be better with the 17 in rim, just for example.

 

As already stated the 17" will be easier to find for a cheaper price and a lighter weight. I myself are privy to the 17" rim. I have a 17x9 enkei that I'm running with a set of 245 40 17 tires. They are a bit undersized for the rim but they had at least a year left on the tread and had sold my wrx summer wheels. Ive also read that the 17 performs better for applications such as autox

 

I'll add that overall tire diameter affects longitudinal grip(accel, braking) more, while wider wheels and tires mostly improve lateral grip(cornering). So if you're concerned about putting power down, a larger diameter wheel/tire will do more for you.

 

You don't want to increase tire diameter. Wheel diameter doesn't affect tire diameter.

Larger wheels are generally bad for handling and ride.

Remember F1 cars fit 10 inch diameter front wheels. They handle really well but the ride is awful...