Salvation is unconditional?

It says that God hates sinners. We are all sinners and it is only by God choosing us, that we become HIS children, Christians. The others who God did not chose, do not elect to become HIS children, they will deny HIM. Salvation is not unconditional in that not all the world will be saved, but it is unconditional in that people of every ethnic group can be saved. Once we become Christians, children of God, then all our past sins are erased and expunged from the records. It is as if our crimes are remembered no more. So it is conditional in that we have to accept HIM and it is unconditional in that it is open to all.