LOL...I know what you were doing! My instructors called it the "Follow the leader syndrome"...instead of looking at the line your are supposed to take...you look at the guy in front of you and take his line! OR it was because you are driving a FWD car (I wouldn't know that line as I have never had one on a real track...Gran Turismo/Forza don't count I think
).
For your purposes that should be all you really need as far as upgrades. Just be aware that once you get really fast with the car it WILL start to understeer (push/slide towards the outside of the corner) a LOT. It is manageable of course but it will happen. You cant do much about it except to slow down more before the curve.