when changing wheel diameter you will want to buy new tires which will maintain the tire's outer diameter (so that they will fit, and the speedometer and gearing won't be adversely affected)
There are lots of tire calculators on the internet, here are a few:
The best tire size calculator. Use our tire size calculator to find tire size specs and suggested tire sizes. Then check prices for all available tire sizes.
Note that fitting larger diameter wheels will increase the unsprung weight (large diameter wheels typically weigh more than small diameter ones do) so the handling will suffer, slightly. Also note that the resulting shorter sidewall will make the ride slightly harsher (cars from the factory with low profile, heavy wheels have specially tuned suspensions to deal with it).
F1 cars have run 13" rims all these years because they provide them the best balance of handling and weight. They will be increasing to 15" soon, in an effort to reduce cornering speeds.
Large diameter wheels on modern cars is a fashion thing, and everyone has their own idea of what looks good (think shoes and wrist watches).