What about predestination?

One of my new friends sent me a short question today, asking for my thoughts on predestination. You know, just a little conversation starter. :)

I've thought about it often and at length, but it's still so hard to formulate an adequate discussion on God's role in our lives and eternal destinies.

I think my response to predestination is looking at it from a human level: since I don't know whom God has determined is His child, I just have to encourage that everyone respond to the Gospel. I live out my belief in free will, because that's how humans experience life: making choices, choosing Christ. But I know that God already knows, because He has chosen who will believe and who won't. 

The hard part for me is, I wonder why God chose one person and not another. Like my cousins' grandma who died without receiving Christ: why did God not chose her to be saved? He certainly could have convinced her of His plan, through what she heard at church and from her family. So I'm still struggling with passages that say God doesn't want one person to perish, and the fact that some people die without believing in Christ when He could have stopped it. 

It's heavy-duty stuff. Now I'm interested to hear what you think on the topic!