I was constantly spinning out too til I put ASM, Skid Recovery and Active Steering on. I had ABS on at 3 and Traction Control at 5, but don't think they matter too much tho. It's difficult with a controller because you have much less throttle control than using pedals, so it is much easier to over-rev and spin.
I'd recommend going into practice mode on each of the circuits before you do the Championship too, so you know how to alter the car for each race (gear ratios and ride height mainly I found).
Pray for rain on the last 2 races too, the AI pitted about 3 times each race to change tyres and I was still out-pacing them by a second or two per lap. That's where the skid assist and ASM really helped I think.
Now I've beaten them using assists I'm going back and trying without, but it is tough.