This discussion could go on for years. It is biblical that God chose us, we don't choose him, and you can find many verses supporting this. But people continue to ask about our choices made in life, about how we must "choose" to become a follower of Christ.
I have a theory, which helps me understand this, and you can read it and devise your own opinions afterwards.
The thing that we as humans often can't get our mind around is Time. God created Time, a time-line, the space-time continuim, whatever you want to call it, He created it. And He is not bound by it. He sees everything at once, from day 1 until the final days of the 7 year Tribulation and the Battle at Megido. He sees it all at once. So He knows our choices before we make them. He chooses us, and since He is omnipotent, He can make us choose Him, or see to it that we choose Him. He knows our choices before we even have them, let alone make them.
So yes, we choose God. But He chose us LONG before time began, as the Bible states. So are we predestined? Yes. Do we elect to accept or reject Christ? Yes. How do both of these work together? Faith. Faith in an all-powerful God who is in complete control and only allows things to happen to glorify Himself. Since we are human, we may not understand how this is possible, but that does not mean it isn't possible.
Just my viewpoint....