Well, you've already thought of the cow problem, so there's probably not much I can tell you...
Everyone will say, "Just go out and have fun." I agree. Go out. Be social. Ask questions. As you drive more and learn more, some things will make sense to you. If you decide you love it, you will thirst for more knowledge.
Actually, you bring up some good points.
1) Brake before the turn. Yes. If you find yourself pushing through the corner, it is often because you saved braking for too late. The front tires are at their max grip, the suspension is unsettled, and now you are asking the car to turn? Take it easy on the next one, brake just as hard, but a little sooner, to allow the car to settle into a better attitude for cornering. Then accelerate through the turn. This is esp. true for nose-heavy, FWD cars like ours.
2) If you make a mistake, don't get frustrated and try to "make up time" by driving even harder. Smoothness and consistency. "Drive slow to go fast," is something you'll hear a lot. It means to be smooth on your control inputs. Don't stab the gas pedal. "Squeeze" it. That sort of thing.
3) If you've never autocrossed before, check out
The Solo II Novice Handbook. It is an excellent resource for the newcomer, covering what to bring, what to expect, and how to behave (etiquette) as well as a few pointers.
I can't possibly cover everything here, and I'm no champion driving instructor, either, but again, HTH.
Enjoy!