I bought my GTi used and it came with a full, new set of the sort of budget tyres mentioned here... I had no confidence in it, you couldn't use the power in a straight line let alone carry speed through corners, or maintain a consistent high(ish) speed with confidence. I learned most of that on the way home from picking it up. In some moments I wondered if the car had a fault, but convinced myself it was the tyres.
Within 24-hours it was in Costco having PS4's fitted and it suddenly felt exactly how I expected it to. Money very, very well spent. FWIW, two years and just over 20k miles later, the same tyres are still fitted with plenty of life left.