There are a huge number of informative resources in the new ESV Study Bible. Here's an excerpt from an article called Preparing the Way for Christ; which traces the references to salvation in Christ throughout the books of the Old Testament.
The article gives a brief redemptive historical approach to salvation history for each book of the Old Testament and then lists specific references from almost every chapter of each book (along with related New Testament passages) which anticipate our redemption through Jesus Christ, what God has accomplished for us:
History of Salvation in the Old Testament: Preparing the Way for Christ
After God creates a world of fruitfulness and blessing, Adam's fall disrupts the harmony. God purposes to renew fruitfulness and blessing through the offspring of the woman (3:15). Christ is the ultimate offspring (Gal. 3:16) who brings climactic victory (Heb. 2:14-15). Genesis traces the beginning of a line of godly offspring, through Seth, Enoch, Noah, and then Godâ€™s choice of Abraham and his offspring (Gen. 12:2-3, 7; 13:14-17; 15:4-5; 17:1-14; 18:18; 22:16-18; 26:2-5; 28:13-15).
Through Moses God redeems his people from slavery in Egypt, prefiguring Christ's eternal redemption of his people from slavery to sin.
The righteousness and wisdom of the law of God prefigure the righteousness of Christ, which is given to his people. The anticipation of entering the Promised Land prefigures Christians' hope for the new heaven and the new earth (Rev. 21:1-22:5).
The conquest through Joshua prefigures Christ conquering his enemies, both Satan (Heb. 2:14-15) and rebellious human beings. The conquest takes place both through the gospel (Matt. 28:18-20) and in the destruction at the second coming (Rev. 19:11-21).
The judges save Israel, thus prefiguring Christ. But the judges have flaws and failures, and Israel repeatedly slips back into idolatry (2:19), spiraling downward to chaos. They need a king (21:25), and not only a king but a perfect king, the Messiah (Isa. 9:6-7).
The line of offspring leading to Christ goes through Judah to Boaz to David (4:18-22; Matt. 1:5-6). Boaz the redeemer (Ruth 2:20), prefiguring Christ, enables Naomiâ€™s disgrace to be removed and Ruth, a foreigner, to be included in God's people (prefiguring the inclusion of the Gentiles, Gal. 3:7-9, 14-18, 29).
David, the king after God's heart (16:7; Acts 13:22), prefigures Christ, in contrast to Saul, who is the kind of king that the people want (1 Sam. 8:5, 19-20). Saul's persecution of David prefigures worldly peopleâ€™s persecution of Christ and of Christ's people.
David as a model king brings blessing to the nation until he falls into sin with Bathsheba (ch. 11). Though he repents, the remainder of his reign is flawed, pointing to the need for the coming of Christ the perfect messianic king.
The reign of Solomon fulfills the first stage of God's promise to David to establish the kingdom of his offspring (2 Sam. 7:12). Solomon in some ways is a model king, prefiguring Christ. But his decline into sin (1 Kings 11), the sins of his offspring, the division and strife between Israel and Judah, and the continual problems with false worship indicate the need for a perfect king and an everlasting kingdom (Isa. 9:6-7) surpassing the entire period of the monarchy. Many passages in 1 Kings have parallels in 2 Chronicles.
Following the history in 1 Kings, Israel and Judah continue to decline through their false worship and disobedience, leading to exile (2 Kings 17; 25). Some good kings (notably Hezekiah and Josiah, chs. 18-20; 22:1-23:30) prefigure the need for Christ the perfect king, while Elisha prefigures the need for Christ the final prophet (Heb. 1:1-3). Many passages in 2 Kings have parallels in 2 Chronicles.
David as the righteous leader and king prefigures Christ the king, not only in his rule over the people of God but in his role in preparing to build the temple. First Chronicles looks back on the faithfulness of God to his people in the entire period from Adam (1:1) to David (3:1) and even beyond (3:10-24; 9:1-34), indicating the steadfastness of God's purpose in preparing for the coming of the Messiah as the offspring of Adam (1:1; Gen. 3:15; Luke 3:38), offspring of Abraham (1 Chron. 1:28; Gal. 3:16), and offspring of David (1 Chron. 3:1; 17:11, 14; Luke 3:23-38; Acts 13:23).
Solomon as a wise king and temple builder prefigures Christ the king and temple builder. After Solomon the line of Davidic kings continues, leading forward to Christ the great descendant of David (Matt. 1:6-16). But many of the later kings go astray from God, and they and the people suffer for it, showing the need for Christ as the perfect king. Hezekiah (2 Chronicles 29-32) and Josiah (chs. 34-35) as righteous kings prefigure Christ. Second Chronicles has parallels in 1-2 Kings but focuses on the southern kingdom (Judah) and the line of David, and it shows focused concern for the temple and its worship, anticipating the fulfillment of temple and worship with the coming of Christ (John 2:19-21; 4:20-26; Eph. 2:20-22; Rev. 21:22-22:5).
The restoration and rebuilding after the exile, in fulfillment of prophecy (1:1), prefigure Christ's salvation (Col. 1:13) and the building of the church (Matt. 16:18; Eph. 2:20-22). They also look forward to the consummation of salvation in the new heaven and new earth (Rev. 21:1).
God providentially brings deliverance to his people through Esther, prefiguring final deliverance through Christ.
Job's suffering and relief prefigure the suffering and glory of Christ.
By expressing the emotional heights and depths in human response to God, the Psalms provide a permanent treasure for God's people to use to express their needs and their praises, both corporately and individually. Christ as representative man experienced our human condition, yet without sin, and so the Psalms become his prayers to God (see esp. Heb. 2:12; cf. Matt. 27:46 with Ps. 22:1). The Psalms are thus to be seen as his words, and through our union with him they become ours.
Wisdom ultimately comes from God and his instruction, which anticipates the fact that Christ is the wisdom of God (1 Cor. 1:30; Col. 2:3) and that in him and his instruction we find the way of life and righteousness (John 14:6, 23-24). Through the Spirit we may walk in the right way (Gal. 5:16-26).
The meaninglessness, frustrations, and injustices of life "under the sun" call out for a solution from God. Christ through his suffering and resurrection provides the first installment (1 Cor. 15:22-23) of meaning, fulfillment, and new life (John 10:10), to be enjoyed fully in the consummation (Rev. 21:1-4).
Song of Solomon
The Song of Solomon depicts marital love. But after the fall merely human love is always short of God's ideal, and so we look for God's remedy in the perfect love of Christ (Eph. 5:22-33; 1 John 3:16; 4:9-10). The connection with Solomon (Song 1:1; 3:7, 9, 11; 8:11) invites us to think especially of the marriage of the king in the line of David (Ps. 45:10-15), and the kings point forward to Christ the great king, who has the church as his bride (Rev. 19:7-9, 21:9).
Isaiah prophesies exile because of Israel's unfaithfulness. But then God will bring Israel back from exile; this restoration prefigures the climactic salvation in Christ. Christ as Messiah and "servant" of the Lord will cleanse his people from sin, fill them with glory, and extend blessing to the nations. Christ fulfills prophecy in both his first coming and his second coming.
Jeremiah's prophetic indictment of Israel is largely rejected, prefiguring the rejection of Christ"s prophetic message to Israel (Luke 11:49-51). God's judgment on Israel for apostasy prefigures the judgment that Christ bears as substitute for the apostasy of mankind (1 John 2:2). It also prefigures final judgment (Rev. 20:11-15). Restoration from exile prefigures final restoration to God through Christ (Heb. 10:19-22).
The lament over Jerusalem anticipates Christ's lamenting over the future fall of Jerusalem (Luke 19:41-44). In both cases, Jerusalem suffers for her own sins. But suffering for sin finds a remedy when Christ suffers as a substitute for the sins of his people (2 Cor. 5:21; 1 Pet. 2:22-24).
God judges Israel's apostasy through the exile. Israel suffers for her own sin, and in so doing anticipates God's final judgment against sin (Rev. 20:11-15). But the suffering also anticipates the suffering of Christ for the sins of others. The subsequent blessing in restoration prefigures the blessings of eternal salvation in Christ (Eph. 1:3-14).
Daniel and his friends exemplify the conflict between the kingdom of God and the kingdoms of this world, a conflict that will come to its climax in Christ, in both his first coming and his second coming.
The unfaithfulness of Israel calls for a permanent remedy, which will come in the faithfulness of Christ to the Father and the faithfulness that Christ then works through the Spirit in his people. God's love for Israel foreshadows Christ's love for the church (Eph. 5:25-27).
The day of the Lord, the day of God's coming (see note on Isa. 13:6), brings judgment on sin but also may include blessing. Both aspects are fulfilled in both the first coming and the second coming of Christ.
God comes to Israel with both judgment for sin and promises of restoration. The judgment and restoration anticipate the crucifixion and resurrection of Christ, as well as the final judgment (Rev. 20:11-15). The demand for righteousness is fulfilled in the righteousness of Christ (Rom. 8:1-4).
The judgment against Edom, a traditional enemy of Israel, contributes to the blessing of God's people. The judgment and vindication prefigure the vindication of Christ and the judgments against his enemies, both in his first coming and in his second coming.
Jonah's rescue from death prefigures the resurrection of Christ (Matt. 12:39-40). The repentance of the Ninevites prefigures the repentance of Gentiles who respond to the gospel (Matt. 28:18-20; Luke 24:47).
God pronounces judgment on Israel, prefiguring final judgment (Rev. 20:11-15) and the judgment that fell on Christ (Gal. 3:13). He promises blessing through the Messiah, anticipating the blessings of salvation in Christ (Eph. 1:3-14).
Judgment on Nineveh, a traditional enemy of God's people, prefigures final judgment and final release from oppression (Rev. 20:11-21:8).
God's use of a wicked nation to accomplish his righteousness foreshadows the use of wicked opponents to accomplish his purpose in the crucifixion of Christ.
The rebuilding in the time of the restoration from exile prefigures the eternal salvation that comes in Christ.
Disobedience and compromise are eliminated with the coming of Christ and his purification.