Run your car as-is. Find out where your weaknesses are, and then modify accordingly. No sense spending $$ on something that isn't your weakest link
Do you know anyone more experienced who will be competing with you? If so, see if they would be willing to help you with the walk-through. If not, maybe someone helping to run the event would be willing to help. Complete the walkthrough multiple times (the last thing you want to do is get lost in a run).
Swallow your pride. Have a more experienced person do a ride-along with you through at least the first heat. If someone more experienced is willing to let you ride-along with them, do it.
If possible, have someone record your runs. This will give you a 3rd-person perspective of your driving.
As long as the course allows it, get the car in 2nd gear and leave it there for the remainder of the course. Focus on driving rather than shifting.
When was the last time you did a brake fluid change? If it's been a while, do one with some quality fluid (e.g., ATE Super Blue).
Most of all, have fun!