Predestination or not?

There is a debate out there about whether we get to choose God or does God choose us. There is some difficulty that people have with the things that God has in his book.

For example, God tells Moses to go to Pharaoh and tell him to let the Israelites go free. But then God tells Moses but Pharaoh will not listen for “I will harden his heart”.
How do we reconcile this?
Did God choose who will end up where before we were born? Are we stuck? Or do we get to choose our own paths.
And if it was God’s choice then doesn’t that absolve us of sin? It was God’s choice not mine. That makes God capricious and cruel.
If it was “my” choice then doesn’t that mean that when I choose to follow God it is not by any action on his part? And doesn’t that, by inference, mean that he is a weak God who can be ruled by MY whim?

Well I do not see the God of the bible sitting around wringing his hands going “gosh I sure hope they pick me.”
At the same time I know that God’s nature means that he is NOT cruel but a loving God. And my “sense of fairness” means that I think it would be wrong of anyone to force someone to commit a crime and then punish them for it. (“If you who are sinners provide good things for your children, won’t God, who is perfect, do more so?”)
So how do we reconcile this?

In my humble opinion it comes down to "free will" (again this is my opinion).
I believe that God wants us to freely choose to obey and follow him. Else why put the tree of the knowledge of good and evil in the garden with Adam and Eve?
As a parent I know that it pleases me when my children choose to obey me rather than when I have to "make" them do what I want/need them to do.
Sometimes in order for them to learn the lesson of obedience I have to allow them the chance to disobey.

If God is our perfect heavenly father then how much more is it the same way with him?
Of course the Fact is that God, as I understand it, is omniscient. ("I am the Alpha and the Omega, the beginning and the end.") He transcends time and knows what will happen in all times. (Thus the ability to give people the gift of prophecy.)
So he knows already what choice/s we will make he has seen it. But because he has given us the option to choose he cannot correct it.

By the way when I say he cannot correct it, what I mean is that while he is the creator of the heaven and the earth and all that exists he cannot go against his own rules.
It seems to me to be very dangerous to make blanket type statements. IE: there isn't anything that He cannot do or accomplish.
A simple (ridiculous) question shows that to be a difficult position to maintain. "So then can God make a rock that he can't move?”
If you say no then obviously he cannot "accomplish" anything. He cannot make a rock he cannot move.
Then again if you say yes, then he cannot accomplish "anything" because there is a force in the universe greater than he is. (The hypothetical rock).
God will not go against his nature, his rules. Therefore since one of his rules seems to be to let people choose for themselves whether they will serve him or not (Joshua 24:15) he will not interfere in that. But because he has the ability to know the choice we will make, he can "call" those who will choose him.
Which, by the way, also means that since he is the one actively seeking us, it is by his mercy through his grace that we are saved so that Paul was able to say "we might not boast".