If you look at the specs for any tire it'll have a recommended rim width range, and also something called the measuring rim width. The measuring rim width is the width of wheel you need to mount the tire on so the tire will be the actual width as quoted in its size. So just as a random example, a Yokohama Advan Neova AD07 225/45-17 has a rim width range of 7 to 8.5 inches, and a measuring rim width of 7.5 inches.

Now when you're talking about what size rim to put with what size tire to get it to look "just right," generally you want to go for the mearuing rim width. This depends however, on how stiff the sidewalls are. A tire with softer sidewalls is going to have a bit of bulge at the measuring rim width so you might want to go a half inch wider to give it some stretch. A tire with really stiff sidewalls is gonna look more squared off at its measuring rim width, but a little bit wider rim isn't gonna make it look too stretched and it'll tighten up the handling a bit.

Now you only want to stretch yer tires so much. 225/45-15 on 15x8" wheels isn't particularly extreme. But if you look at what drifters do they stick like, a 215 series tire on a 9" wide rim to give tons of stretch so the tires will break traction earlier. Or VW people will put some skinny ass tire on some wide ass wheel so they can get as fat a lip as possible and still fit the tire under the fender even if the wheel is stickin way past it.

From your second post though it sounds more like you just want to avoid the rubber band look than to avoid stretch or bulge. That mainly has to do with the sidewall height of the tire. Whatever the stock wheel/tire combo is, you need to replace it with something of a similar overall diameter. If you go to a larger wheel you need to go to a thinner tire which is why Civics running 20s look like they're rolling on rubber bands. If you're just going from 16" stock WRX wheels up to 17" replacements, you still have room for a reasonably thick sidewall so as not to look too dopey.