Here's a link to performance summer tires in these sizes from tirerack
https://www.tirerack.com/tires/TireSearchResults.jsp?zip-code=90001&frontWidth=205/&frontRatio=55&frontDiameter=16&rearWidth=225/&rearRatio=50&rearDiameter=16
I've been very happy with my continental extremecontact dw tires (predecessors to the EXTREMECONTACT SPORT which is well below your pricerange)
Have also heard good things about the Bridgestone RE-11s
Although the Michelin Pilot Exalto PE2 tires are just out of your price range, they are NOT all season and are porsche-certified (which is SUPPOSED to indicate that they're specifically developed for use in our cars) --