It is quite difficult to comprehend why many of us like to think about individual predestination when the apostles Paul and Peter were really saying that God had predestined to offer redemption to the Gentiles. When Paul wrote that God had chosen us before the foundation of the earth, he was really emphasizing that way, way back, God had always planned to offer redemption to the Gentiles. And we should know that Paul was saying this because many Jewish Christians were upset that Gentiles were allowed to be part of the gospel, which was a drastic departure from the past.
About the words "chosen people" or "Chosen by God": We tend to interpret factually today, thinking that God handpick or choose who should be saved. However, during biblical times [2000 or more years ago), people were more submissive to God -- much much more than people today (it must be noted). Back then, they don't say that they chose to believe in Him; instead they said that God chose them. It is a humble way of speaking. To say that they chose to believe in God would have sounded arrogant or inappropriate. Today we don't speak that way anymore, and to us now, such words sound like God literally choose who to save. But back then, it was really a humble way to say that it was a privilege to be part of God's people or kingdom.
Regarding predestination: Many Christians have been so awed by the word predestination that we forgot about context. Predestination means pre-planned. In biblical context, it means that God has pre-planned to offer redemption to the Gentiles. Paul or Peter were NOT talking about predestination of individuals.
For 2000 years before the apostles' times, Yahweh was God to the Jews only, while other pagan nations worship many pluralistic gods. Even after Jesus' resurrection, the apostles initially thought that redemption was intended for Jews only. Then Peter received a vision about eating unclean food, and they realized God wanted them to preach the gospel to the Gentiles too. Now, this was shocking to the Jews because it went against their tradition which was so rooted in the God of Abraham and Jacob, where Gentiles had no part in their God. As the old order changed, the Jews were displeased, and they demanded that Gentiles followed Jewish customs (many Christian Jews were still practicing circumcision and Sabbath at that time). Amid the hostility, even Peter distanced himself from the Gentiles, and Paul opposed Peter for that. To assure the Gentiles, Paul explained in Ephesians (and Letter of Romans) that God had always predestined (pre-planned) to offer redemption to the Gentiles. Let me explain the following verses while quoting them:
Ephesians 1:12, 13
[12]"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, in order that we, who were the first to put our hope in Christ, might be for the praise of his glory.
===> "we, who were the first to hope in Christ" refers to the Jews who had believed in God for 2000 years
[13] And you also were included in Christ when you heard the message of truth, the gospel of your salvation
==> The Gentiles, who were previously excluded from Christ, are now included. Notice how Paul used different pronouns "we" [v 12] and "you" [v 13] as he refer to the Jews and Gentiles respectively.
When seen in context, the Bible was not talking about predestination of individuals. Instead, predestination means God has always planned (or pre-planned or predestined or destined) to offer redemption to the Gentiles. Different translations use different words but when we know context, we will not drill into the words technically.
