As a high school student, this is beyond anything you need to know. Nevertheless, let me clear some confusions.
Minimum free energy does represent the state of maximum thermodynamic stability, and it is decreased when enthalpy is minimized and entropy is maximized. However, the idea that stability increases as enthalpy decreases because that is a decline in potential energy is wrong.
According to conservation of energy, and decrease in the energy of the system has to be balanced out by an increase in the energy of the surroundings because the energy of the universe is constant. This means that part of the universe (system) has a decrease in energy while the other part of the universe (surroundings) has an increase in energy. Since we define the boundary between the system and the surroundings, it simply cannot be true that a decrease in energy is a driving factor for thermodynamic stability. Why would something favorable (decreasing energy) happen for one part of the universe while something unfavorable (increasing energy) happen for the rest of the universe?
What drives thermodynamic processes is entropy, which is really probability. Entropy of the universe can only stay constant or increase. Any process that happens in the universe results in an increase in entropy. This is why maximization of entropy is a favorable factor in minimizing free energy. The reason a decrease in enthalpy is favorable is because a decrease in enthalpy of a system is approximately an increase in entropy of the surroundings. If the entropy change of the surroundings is added to the entropy change of the system, then you get the entropy change of the universe. If this entropy change of the universe is positive, you get a spontaneous process, which is (approximately) the same thing as a negative change of Gibbs free energy of the system.
http://en.wikipedia.org/wiki/Gibbs_free_energyMost of this probably didn't make sense to you, and that's ok. Thermodynamics (physical chemistry) is not something you study until late into your chemistry degree.