A Partial set of notes and Scriptures: 

(Joh 3:16)  For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.
1Ti 2:1  Therefore I exhort first of all that supplications, prayers, intercessions, and giving of thanks be made for all men, 
1Ti 2:2  for kings and all who are in authority, that we may lead a quiet and peaceable life in all godliness and reverence. 
1Ti 2:3  For this is good and acceptable in the sight of God our Savior, 
1Ti 2:4  who desires all men to be saved and to come to the knowledge of the truth. 
1Ti 2:5  For there is one God and one Mediator between God and men, the Man Christ Jesus, 
1Ti 2:6  who gave Himself a ransom for all, to be testified in due time, 
1Ti 2:7  for which I was appointed a preacher and an apostle—I am speaking the truth in Christ and not lying—a teacher of the Gentiles in faith and truth. 

Heb 2:9  But we see Jesus, who was made a little lower than the angels, for the suffering of death crowned with glory and honor, that He, by the grace of God, might taste death for everyone. 
Heb 2:10  For it was fitting for Him, for whom are all things and by whom are all things, in bringing many sons to glory, to make the captain of their salvation perfect through sufferings. 

Call, Called = gk. Invitation

(Act 2:39)  For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call."
Chosen = gk, eklektos
(Mat 20:16)  So the last will be first, and the first last. For many are called, but few chosen."

Holy, Haggios 

(Joh 6:44)  No one can come to Me unless the Father who sent Me draws him; and I will raise him up at the last day.
DRAAAAAGS him... :)

So, what is THE PROCESS?  Point 3 
(Joh 6:64)  But there are some of you who do not believe." For Jesus knew from the beginning who they were who did not believe, and who would betray Him.
(1Co 2:14)  But the natural man does not receive the things of the Spirit of God, for they are foolishness to him; nor can he know them, because they are spiritually discerned.
(1Co 2:15)  But he who is spiritual judges all things, yet he himself is rightly judged by no one.

What about our Children? We must teach them till they grow.

Act 2:38  Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. 
Act 2:39  For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call." 

Mat 13:10  And the disciples came and said to Him, "Why do You speak to them in parables?" 
Mat 13:11  He answered and said to them, "Because it has been given to you to know the mysteries of the kingdom of heaven, but to them it has not been given.