“There is a third possibility of doing good deeds because it’s the right thing to do. I guess you could say that this involves following the Golden Rule, but without believing in the supernatural.”
Here’s the issue with that...
If you don’t believe in God, how can you know what “good” is?
Where there is no standard-bearer there are no standards!
1. "What is hateful to thee, do not unto thy fellow man: this is the whole Law; the rest is mere commentary." - Hillel the Elder
2. It is not necessary to believe in (or to be afraid of) a supernatural being in order to always follow #1 as a part of one's nature. It's does help to be raised by loving parents who very early teach about right and wrong. But I noticed that my 4 year old son already had a very powerful sense of morality, so I wonder if some of it is innate.