You will find that most of your cone strikes will be with the rear of the car. As JRJ is saying, late apex is your friend. In autocross terms, "back-siding the cone".

On the course walk. Walk where you (not the center of your car) will be. You should be right next to the cones on the left and 4 ft away from the cones on your right.
Find the fastest section or two. Then do everything you can to come out the preceding element as quickly as possible. Even if it means going in extra slow.
Find the slowest section. Then realize it is going to be slow no matter what. Don't try to make it fast. Just keep it tidy. You can lose a lot of time trying to take a 20mph turn at 21 mph..
Almost always, the shorter distance is faster than carrying speed in autocross. Unlike a road coarse.
A little bit of slip angle. Never drift.........well if you want a fast time. It sure is fun though.

You should be looking very very far down course. Way more than a couple cones. I went to an SCCA Starting Line autocross school run by two national champions. They had us walking the course. One of the instructors walked crazy far down course and then they said , "That is where you should be looking". I thought I WAS looking down course. But needed to double it. I was also looking at apex cone on a turnaround, and have since learned to look at the exit cone as I am entering.

Here is a little warm up that I do on the way to the event, if you have open road. I move over until I am just clipping the lane reflectors on one side then the other a few times. As I am moving over I try to nail exactly when I will start hitting them. That helps with refreshing my memory on where the outer edges of my car are.