. . . because we have put our hope in the living God, who is the Savior of all people, and especially of those who believe.
1 Timothy 4:10 NIV
Who will be saved? There are roughly three schools of thought concerning this question. The first response is that, in the end, everyone will be saved. And this verse (God is the Savior of all people) is sometimes used to support that position. 2 Peter 3:9 (God does not want anyone to perish) and 1 Timothy 2:4 (God wants all people to be saved) are also used to support the idea of universal salvation.
Yet this verse distinguishes between those who believe and those who do not. God is especially the savior of those who believe. John 3:16-18 says that God so loved the world that he sent his Son to be our savior. Those who believe in him will have eternal life, while those who do not believe will perish. While God offers salvation to all, only those who believe experience that salvation.
A second response to this question is that all those God has chosen will be saved. This position generally limits the universal scope of salvation mentioned in the passages above to a more limited number of people. And all who are included in that select company will be saved.
Yet passages like this one, John 3:16 (for God so loved the world), 1 John 2:2 (Jesus is the atoning sacrifice for us and the whole world), and 1 Timothy 2:6 (Jesus gave himself as a ransom for all people), point to the work of Jesus as being universal in scope.
So, who will be saved? Those who believe. Salvation is offered to all people. But only those who believe will be saved. God is the savior of all people (universal in scope), especially those who believe (limited in effect).