There are three things here. First, God does not choose the sins we commit in the sense of causing them to happen by giving us a booster shot of evil toward a particular purpose. That is not His nature. God, already knowing our nature, allows sin to take place for His purposes. The sin act comes just from us.
Second, God created us allowing for our fallen nature through Adam. Our nature is to sin. No man except Jesus has not sinned. (For all have sinned and fall short of the glory of God.) If you are referring to a particular sin at a particular time, then God may or may not open certain doors He already knows the sinner will enter (e.g., Judas). But, God does not cause the sin, He allows it.
Third, we are "condemned to sin" from the moment of our conception. That's Adam's fault, not God's. Of course, that's just the bad news. The Good News is ... (well, you know :)