New wheels what tire
 

245/40-18

Do you expect to drive on this tire during a Wisconsin winter?
Are you planning on any actual performance driving on track or AX or just cloverleaf interchanges and traffic circles?
How much money do you have to spend?
How much NVH can you stand?

I like Yokohama S-drives as my daily tire. They're an oldish model, but they do everything well.

I've been a fan of the Bridgestone Potenza S-04 Pole Position for a while.

Also, there's a rabid fanbase (which I'm not a member of) for the Michelin Pilot Super Sport. It's about 10% over your budget but you're likely to hear about it at some point. Nothing wrong with the MPSS if you have the money to spend. As I understand it, the Michelin Pilot Sport 4S is also a very good tire.

Of course, if you want premium grip and don't care about noise (or treadlife), the Bridgestone RE-71R, Hankook R-S4, Kumho V720, Dunlop DZIII, Falken 615k+, Nexen Nfera SUR4G are all top-performance models.

Edit:
Wait, no track days? Why not?!? Your state is home to Road America!!!
IMO, you haven't truly appreciated your car until you've had it out on a track.

I have a set of Falken Fk 453 right now, which is okay for street use. Do anything above that(like AutoX or tracking), they won't keep up all that well. I do spirited DD and casual AutoX(don't care if I come in last).

They are wearing out, though. I have about 3~4 mm(5/32 in) left. I plan to have a set of Firestone Indy 500 next.

If you AutoX, you will likely hear about the Bridgestone RE71-R. The local one I attend has a lot of people using them. They are great for AutoX, which is like under a minute per run and you have a good amount of time to cool down before your next run. However, their performance will degrade rapidly should you take them to a track. Supposedly they give you about 10 minutes of solid grip and then they will start to feel like there is grease on them.

You will definitely need a helmet. AutoX already requires it. You can grab one at your local motorcycle store. Make sure it has the right certifications.

You may need a roll cage but I am not 100% on that. I know it's a must on a convertible, not sure about hardtops.

For a basic, non-competition trackday, most places only require a helmet and closed-toe shoes. Some may require long sleeves and pants but not all. If you want to do time trial stuff, then cages may be required. Most groups will require a recent SNELL M or SA helmet (SCCA is usually within the last 15 years so M2005 and SA2005 are good until 2020 and then M2010 or SA2010 will be the minimum).

You'll go through tech inspection where they'll make sure your ball joints aren't falling apart, tires aren't showing cord, battery is secured down, etc. But it's regular road cars. My '8 doesn't have any extra safety gear.

Trackdays can be expensive but the Chicago Region of the SCCA only charges $150 for a half day (three 20-minute sessions) at Autobahn Country Club in Joliet, IL and $250-$275 for a full day (6 sessions) at Black Hawk Farms in South Beloit, IL. Events at places like Road America are typically a bit more expensive because RA is a more expensive facility to rent out.

Look up MVP Track Time, Track Night in America for nationwide groups. The Milwaukee Region of the SCCA is also pretty active (and has some wicked fast drivers you can learn from). Home - Milwaukee Region SCCA
If you aren't near Milwaukee then check out the SCCA website to see if there is a group closer to you.

thank you everyone definitely going to look into it