You'll always have a compromise between a tire that will work well at autox and a tire that will work well on the street.
If you push a comfortable street tire at numerous autox's you will often start to see things like extreme wear on the outer edges, heavy feathering and even chunking of tread.
A dedicated autox tire that will perform will on course will have compromises in ride comfort, rain capability and have zero chance in snow/ice on a daily basis.
A common solution is to find some cheap used stock wheels and slap on some dedicated autox rubber. Just giving you the idea, but it will depend on your budget and how serious you get into the sport.
Parking Lot Hero
2008 WRX daily driver
2003 ZX3 23D Autox Car 42 FSP
"Hella Functional - Raced, Not Hard Parked"