I found a great article on the Society of Evangelical Arminians website here that explains quite brilliantly, along with supporting scriptures, the biblical notions of Election and Predestination. Here are some excerpts:
Concerning election and predestination, we might use the analogy of a great ship on its way to heaven. The ship (the church) is chosen by God to be his very own vessel. Christ is the Captain and Pilot of this ship. All who desire to be a part of this elect ship and its Captain can do so through a living faith in Christ, by which they come on board the ship. As long as they are on the ship, in company with the ship’s Captain, they are among the elect. If they choose to abandon the ship and Captain, they cease to be part of the elect. Election is always only in union with the Captain and his ship. Predestination tells us about the ship’s destination and what God has prepared for those remaining on it. God invites everyone to come aboard the elect ship through faith in Jesus Christ. [Life in the Spirit Study Bible, pp. 1854-1855]
Election (Gk eklego) refers to God choosing in Christ a people whom he destines to be holy and blameless in his sight (cf. 2 Th 2:13). Paul’s teaching about election involves the following truths:
(1) Election is Christocentric, i.e., election of humans occurs only in union with Jesus Christ. “He chose us in him” (Eph. 1:4; see 1:1, note). Jesus himself is first of all the elect of God. Concerning Jesus, God states, “Here is my servant whom I have chosen” (Mt 12:18; cf. Isa 42:1, 6; 1 Pet 2:4). Christ, as the elect, is the foundation of our election. Only in union with Christ do we become members of the elect (Eph 1:4, 6-7, 9-10, 12-13). No one is elect apart from union with Christ through faith.
(2) Election is “in him…through his blood” (Eph 1:7). God purposed before creation (Eph. 1:4) to form a people through Christ’s redemptive death on the cross.
(3) Election in Christ is primarily corporate, i.e., an election of a people (Eph 1:4-5, 7, 9). The elect are called “the body of Christ” (4:12), “my church” (Mt 16:18), “a people belonging to God” (1 Pe 2:9), and the “bride” of Christ (Rev 19:7). Therefore, election is corporate and embraces individual persons only as they identify and associate themselves with the body of Christ, the true church (Eph 1:22-23)
(4) The election to salvation and holiness of the body of Christ is always certain. But the certainty of election for individuals remains conditional on their personal living faith in Jesus Christ and perseverance in union with him. Christ will “present you holy in his sight without blemish…if you continue in your faith, established and firm, not moved from the hope held out in the gospel” (Col 1:22-23).
(5) Election to salvation in Christ is offered to all (Jn 3:16-17; 1Ti 2:4-6; Tit 2:11; Heb 2:9) but becomes actual for particular persons contingent on their repentance and faith as they accept God’s gift of salvation in Christ (Eph 2:8; 3:17; cf. Ac 20:21; Ro 1:16; 4:16). At the point of faith, the believer is incorporated into Christ’s elect body (the church) by the Holy Spirit (1 Co 12:13), thereby becoming one of the elect. Thus, there is both God’s initiative and our response in election (see Ro 8:29, note; 2 Pet 1:1-11).
Predestination (Gk prooizo) means “to decide beforehand” and applies to God’s purposes comprehended in election.
(1) God predestines his elect to be: (a) called (Rom. 8:30); (b) justified (Ro 3:24, 8:30); (c) glorified (Ro 8:30); (d) conformed to the likeness of his Son (Ro 8:29); (e) holy and blameless (Eph 1:4); (f) adopted as God’s children (1:5); (g) redeemed (1:7); (h) recipients of an inheritance (1:14); (i) for the praise of his glory (Eph 1:2; 1 Pe 2:9); (j) recipients of the Holy Spirit (Eph 1:13; Gal 3:14); and (k) created to do good works (Eph 2:10).
(2) Predestination, like election, refers to the corporate body of Christ (i.e., the true spiritual church), and comprehends individuals only in association with that body through a living faith in Jesus Christ (Eph 1:5, 7, 13; cf. Ac 2:38-41; 16:31).