Who did Jesus die for and who can be saved? What do you think the Bible teaches? Part I

To many people the three views described below will look very similar, but they can have quite a significant impact on what people think God is like and on how you share the Gospel with people.

I have held all three views, initially the first, then the second, followed by the third and then back to the second on which I'm now fairly settled, but I recognise that I could have got this wrong. 

I'd love to know what view other people hold on this. My hunch is that most pastors among my friends will hold the third view, but that most church members will hold the first or second view. 

First view

Through the life, death and resurrection of Christ, God has made salvation available to every single person in the world. Everyone who believes in Jesus will be saved. Those who do not believe will not be saved . Every single person who hears the gospel is capable of believing in Jesus. God gives people a new heart as a result of their faith in Christ. The new heart is not the cause of the person first putting their faith in Christ, but the result of the person's faith in Christ.

Second view

Through the life, death and resurrection of Christ, God has made salvation available to every single person in the world. Everyone who believes in Jesus will be saved. Those who do not believe will not be saved. Because of original sin, no one has the capacity to put their faith in Jesus, unless God first works in them to give them a new heart. Everyone, in whom God puts a new heart, will put their faith in Jesus and be saved. The refusal of others to accept the salvation that is freely made available to them through Jesus' death shows the depths of the effects of original sin.

Third view

Through the life, death and resurrection of Christ, God has made salvation available only to the people he has chosen. All those he has chosen will believe the gospel and be saved when God gives them a new heart. There are many people for whom Christ has not died, and so, although all people should be called to repentance and faith and all people should be assured that if they believe in Jesus they will be saved, the evangelist should not tell non-Christians that Jesus has died for them because this may not be true in the case of the particular person to whom the evangelist is speaking.