"Will higher octane or premium fuel give me better gas mileage and/or more power?"

No, not necessarily. You see, sportier cars typically have higher compression engines.  "Octane", as it pertains to fuel, is an additive that actually prevents combustion-- that is, it prevents premature combustion from compression.  If the fuel/air mixture in these high-performance engines is detonating too early from the sheer pressure inside the cylinder, then the engine will not produce optimal power.  Higher octane gasoline prevents the mixture from detonating until it is provoked into doing so by the spark plug.  That's where the myth of "premium = more power" came from. If your handbook says "regular", use regular-- you will see no benefit in using higher octane fuel.