I'm not sure what the cutoff is, but it's damn sure not any vehicle running 13s stock.
Most of your recommendation was spot on, just not the turbo part. I suggested earlier a NA Impreza hatch. All of the suspension mods from a WRX/STI will bolt right up, but it's not fast enough to make doing something retarded a temptation, and it's not nice enough to draw hate in the parking lot.
That's one of the benefits of never having had a car before- whatever you get, it's the fastest car you've ever had.