I had the Falkens on my Boxster and liked them, but they got greasy when hot and did not last long. The PS2's on my GT3 chunked badly when hot. I was very happy with the Advan Neova's on the GT3, and still have them. They stick great, take the heat, wear evenly, and are only a few seconds slower than Hoosiers. They are a little expensive, but again they last a long time. If you end up with Toyo's, don't be surprised. Learn to read your tires visually by wear and roll-over. Ask some instructors how they do it.
On the Boxster, I increased the front widths by 20 mm (225->245)and reduced the rear by 10 mm (255->245) and the car would drift beautifully around high speed sweepers. It was a wonderful thing. The understeer was gone. And don't let those pressures build up too high.
Also, as mentioned, the performance alignment will make the car turn in much better. Don't forget about Jae and Dave at Mirage, along with Dieters and Black Forest. They are all great with suspensions.
Be sure to ask the Boxster guys like Kim Crosser and Charlie Kleinhans (LSS) or Carl Vanderschuit and Pierre Maurier (LS). They have been working this platform for years and know it pretty well. If you can beat them with your extra horsepower and rigid chassis, you should be proud.
Good luck. Whatever tires you put on are not going to be there very long, so you get lots of second chances to change your mind.