This is a heavily debated topic in the history of the church, so it's worth saying at the outset that however one lands on the subject, Christians can disagree on this in good faith. It is sad that predestination has become such a heated subject, when it is something that we should be deeply humbled by.
Christians, no matter their theological leanings, should believe in predestination. That's a bold statement! But it's inescapable, if only because the bible actually uses the word itself. So the debate is really about what the word means biblically and theologically.
The key texts would include:
Matthew 22:14: "For many are invited, but few are chosen."
Ephesians 1:4-6: "For he chose us in him before the creation of the world to be holy and blameless in his sight. In love he predestined us for adoption to sonship through Jesus Christ, in accordance with his pleasure and will—to the praise of his glorious grace, which he has freely given us in the One he loves."
Ephesians 1:11: "In him we were also chosen, having been predestined according to the plan of him who works out everything in conformity with the purpose of his will."
Romans 8:28-30: "And we know that in all things God works for the good of those who love him, who have been called according to his purpose. For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters. And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified."
Romans 9:14-16: "What then shall we say? Is God unjust? Not at all! For he says to Moses, 'I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.' It does not, therefore, depend on human desire or effort, but on God’s mercy." [Really, all of Rom. 9]
1 Peter 1:1-2: "To God’s elect, exiles scattered throughout the provinces of Pontus, Galatia, Cappadocia, Asia and Bithynia, who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, to be obedient to Jesus Christ and sprinkled with his blood."
There are more, but I hope these help!