Hi FullMetalShorty - while not as bad as you, i am pretty skeeved by public restrooms and will do my best not to use them. just to echo the advice from the others here

Always flush with your foot.
Never sit down -Always hover but you might want to put some paper or one of those seat covers on the seat just in case you lose your balance.

Use a paper towel to turn the faucet on and off and to open the door to leave the restroom.

People have a tendency to use the stalls furthest away from the door, so there may be a few less germs in the ones closest to the door.

I always try to find the ones in nicer places - like the nicer the store, the nicer the restroom - the further out of the way the restroom is, the less it is used, therefore, cleaner.

Good luck!