Sport Tires performs well enough for cars under 500 bhp (M5 came with stock Sport tires and they drive awesome), so for starters, the key is....
Power to weight ratio!!!
Let's say if we have very little money at the beginning, what's the best way to improve the power to weight ratio? Chips? That gets you like 10 bhp max, exhaust??? maybe 20 bhp, and you risk losing low end torque. So what's the best way to improve power to weight ratio? Stage 1 Weight reduction. It only cost 1200 CR and you can lose 10%+ of the weight easily, and this is an investment that won't go to waste. (if you get a stage 1 turbo, you are likely to upgrade to stage 2, 3, and 4 later) and all the previous investment would've gone to waste.