After; piss off the car wash folks. Get the crap out from everything. Leaving the mud, stones, debris in there just gives it more time to work it's evil.
Before: I drove big rigs and we had to do pre and post trip inspections each day.
Common sense stuff. Check the lights, tires (pressure/damage), wipers, look for leaks, look for wear, loose fasteners, look at the brakes, hoses and belt(s) Etc.
I still do a sorta inspection before I jump in the pickup or Jeep. When I walk out of the house I'm on the passenger side of the vehicles, I look at the front end, look underneath, look at the tires, working my way around the back to the driver's door.