David was a man after God's own heart. Jonah was swallowed by a whale. Noah built the ark and saved God's creatures.
Predestination is, indeed, a Biblical doctrine.
The hyper-Calvinists teach that God predetermined, completely independent of every human being's free moral agency, those who would ultimately go to heaven, as well as those who would ultimately go to hell. This is absolutely contrary to Scripture. So it is very clear that man chooses his own destiny by the life he chooses to live. Choosing the Lord and a life of self-sacrifice ends in eternal bliss in the Father's house. Choosing sin and a life of temporal pleasure ends in eternal damnation in the Lake of Fire.