I know you said you don't autox but if you're pushing the car into corners and losing control then you need to autox to learn the limits of the car and how to recover from a spin. Many regions offer novice schools and are usually about $50 and worth every penny of it. The best improvement for a car is usually to upgrade the nut behind the wheel.
As for other modifications it's really up to you. Personally I hold handling above all else so I'd say buy decent tires first. Others will tell you that you need a windshield banner and some clear corners, it's all opinion. If you do turbo it then you will need a good suspension and brakes to handle the higher speeds (preferably installed before you find out you need them).
Just my $0.02.