Don't waste your money on slicks as a beginner. They have more grip but don't give you as much feedback before breakaway, definitely something you should work up to IMO. Street tires are good at teaching you how to drive at the limit of traction as you will be potentially at that limit a lot.
Critical upgrades are as everyone else said, pads, fluid and oil cooler. After doing a couple of events I would go for sway bars next, it is a good intermediate step before coilovers.
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