I’ve run Bridgestone S-02, S-04, Continental Pro Contact, Sport, DW, Michelin Pilot Sport4S, and AS3, and others.
The Tire Rack has a great guide to tires. You can also call them and talk to them. The are really great.
For a cheaper tire that would work great for you, the Bridgestone S-04 is very good.
The Continentals are also great.
Falken Azenis are great in the dry, but like a slick in the rain. But they are very good tires for the money.
A lot of folks here like the Firestone Indy 500, but I have never tried those myself.
Look at the Tire Rack’s “High Performance” tire choices in your size on their web site as a guide.
I put about about 20,000 miles on the Bridgestone S-04 and I liked them a lot. It was a great all around tire for not much money.
I switched from those to the brand new Michelin Pilot Sport 4S and they are my new favorite tire of all time, but holy crap they are expensive.
Good luck, keep us posted.