When our flesh, which is as grass (Isaiah 40:6), understands that it could not choose itself and accepts what God has done to it on the merits of His love for it and the revelation of what He can do through it and despite it, then we can understand what it means to be chosen by God.
Peter tried to choose Christ, but his flesh was as grass. The disciples, though they walked with Christ, saw miracles and even performed some themselves, failed when the true test arrived and forsook Him during His crucifixion. They tried to choose Christ through dedication, because they could not follow through with consistency in their choice. One thing is very clear: they didn't choose Him; He chose them.
Even at salvation, when we discovered that Christ shed His Blood and died for us, we made ourselves available to His choice. When a man tries to choose God, he has the impossible task of trying to be born again of the will of man, rather than the will of God, and subsequently of desiring his will toward God rather than of living in God's will toward him.
Christ has chosen you; you have not chosen Him. He has chosen you to be the object of His grace, the subject of His mercy, the person of His redemption, the place of His habitation, the humanity to and through which His divinity would be revealed. Your flesh will not always be consistent in its choice, but God has already chosen you. You need never experience the dilemma of indecision. He made the decision.