Definitions:
Free Will: The idea that in order to be saved, a person has to choose Christ. This implies NOT (I want to call it Mechanism) the world-view that simple rules of physics govern all action in the universe. It implies NOT that.
Predestination: The idea that in order to be saved, a person has to be chosen by God, and that any person choices they may or may not make (or be able to make) have nothing to do with it. This does not imply either Mechanism or NOT Mechanism.
History:
I always assumed Free Will, since I have a direct experience of making choices every day, and everybody told me that to be saved I had to choose Christ. However, as I grew in mind and learned about the physical laws that govern the way a huge ton of stuff acts (including my brain-chemicals), and read verses that say things like, "God definitely decided that you would go to heaven even before He made the world", I began to doubt this.
Now, doubting Free Will is, in a certain way, to doubt one of my own faculties (Or something that seems very much to be a deep part of myself). Am I really making a choice, or are the chemicals in my brain doing it all, having been set in motion before the beginning of the world by That Great Watch-Maker In The Sky? This is actually comforting, because it means that whatever I did, I couldn't help doing, and whatever I will do, I can't help doing. I can do nothing besides what I will have done. I ovbiously can't be punished for that: Comforting. I suppose, though, that my body could: Painful.
I don't know why I combined Free Will and Mechanism that way. It just seemed like if I couldn't choose about my very salvation, I obviously couldn't choose anything. Since there's a ready-made philosophy already in place for not choosing, I lumped them together. It could be that God lets you choose what to wear on Monday but not whether to follow Christ to eternal life.
So I wavered between the two. Sometimes it seemed like I was choosing, and sometimes it seemed like I was being chosen.
But good news! I have reconciled the two ideas. I understand how they can both be true.
It depends only on God's omnipotence. I will use an analogy in which this is likened to a writer's omnipotence (i.e. whatever a writer writes in his book is real, true, and existant within that book, and for all characters, objects, and things within that book).
So let's say that a writer writes that his character has chosen something by their own free will, and then goes on to describe what it was that they chose. For that character, it is TRUE that they chose by their own free will. Whatever the author writes is true, and the author wrote that he chose freely. ALSO, the author decides what the character will choose, and writes it down.
Summary:
(To God,) God has created man with free will. He has also chosen what we will do, what we will choose, and whether we will end up in heaven or hell. He has to choose all this or else none of it will happen at all without him 'writing it down' as omnipotent Creator-God.
(To man,) Man finds himself with free will, and makes his choices freely.