I recommend getting a set of track wheels+tires (18's preferably) to start. R-compounds will offer more grip and stay driveable for a longer period. Street tires will rapidly decrease performance on cornery tracks, as they get very greasy when hot.
You'll also feel way more comfortable knowing that you'll still have your street tires for "the day after", if you were to go through your set at the track.
Next is race brake fluid and better brake pads.
Then I would look into suspension: camber plates are a must, coilovers eventually.
That should set you up well, until you get more experienced at the track.
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