Ok so I guess you are in the learning process right now if your spinning out. If you are spinning out this means you are going too hard on the throotle and if you are snapping to the opposite side of the corner this means you are counteersteering too much. What you can do when you approach a corner is:
Let's say its a right hand corner, don't go too fast, just do about 50mph. And jab the wheel to the left and then back to the right and let your fingers off so the wheel counteersteers, just as you let of your wheel full throotle for a second and then catch the wheel about halfway and control if you are getting too much angle, less throotle and if you are going into inside and about to spin more counteersteer. I know this probably doesnt make much sense but you can also onboard videos on youtube to help you. BTW a good starter car is the Mazda RX7 FC or FD, fully tune the car except the turbo. Use a low- medium rpm turbo to avoid turbo lag, you dont wanna exceed 400hp. Then buy the 6speed transmission and the all the lsd parts. Set your LSD to 5/60/55. And now Il give you a brief suspension setup that should get you sideways.
Ride height: Slam it at the back, and about -10 in the front.
Spring Rate: 7.5 in front and 5.5 in back.
Dampers: 4 front 3 back
Dampers: 3 front 2 back
Anti-roll bars: 4 front 3 back
Camber: 2.5 front and 0.5 back
Toe: front -0.10 and back 0.00
And finally slap on some comfort hards and practice, practice, practice...
I hope I helped you at least a little bit, if you have any questions feel free to ask.