As far as the best tire, I'll defer on making a suggestion there.
As far as size, 255/50x20 or 245/45/20 would work great. You can go to a 275/40x20 all the way around but the front could rub a bit in a full turn.
Look for a tread wear rating of 300 (sometimes known as the durometer) or higher. The higher the number, the less "performance" you'll get. You end up trading wear for stickiness.
Lots of brands out there to choose from. My experience with the stock Continentals and Goodyears was very, very poor.
Nitto, Michelin, BFG and Falken are all brands I have used in the past with good results. I currently run Toyo Proxes 4 tires, 245/45x20 on the front, 275/40x20 on the rear.
You might also look into the Hankook line. I hear good things about them but have no experience with them.
2006 300C SRT8