Here is an highly competent summary of the Messianic thrust of the Old Testament.
Alfred Edersheim, The Life and Times of Jesus the Messiah, Book 2, Chapter 5, pp.113,114
The most important point here is to keep in mind the organic unity of the Old Testament. Its predictions are not isolated, but features of one grand prophetic picture; its ritual and institutions parts of one great system; its history, not loosely connected events, but an organic development tending towards a definite end. Viewed in its innermost substance, the history of the Old Testament is not different from its typical institutions, nor yet these two from its predictions. The idea, underlying all, is God’s gracious manifestation in the world – the Kingdom of God; the meaning of all – the establishment of this Kingdom upon earth. That gracious purpose was, so to speak, individualized, and the Kingdom actually established in the Messiah. Both the fundamental and the final relationship in view was that of God towards man, and of man towards God: the former as expressed by the word Father; the latter by that of Servant – or rather the combination of the two ideas: ‘Son-Servant.’ This was already implied in the so-called Protevangel; and in this sense also the words of Jesus hold true: ‘Before Abraham came into being, I am.’
But, narrowing our survey to where the history of the Kingdom of God begins with that of Abraham, it was indeed as Jesus said: ‘Your father Abraham rejoiced that he should see My day, and he saw it, and was glad.’ For, all that followed from Abraham to the Messiah was one, and bore this twofold impress: heavenwards, that of Son; earthwards, that of Servant. Israel was God’s Son – His ‘first-born;’ their history that of the children of God; their institutions those of the family of God; their predictions those of the household of God. And Israel was also the Servant of God – ‘Jacob My Servant;’ and its history, institutions, and predictions those of the Servant of the Lord. Yet not merely Servant, but Son-Servant – ‘anointed’ to such service. This idea was, so to speak, crystallised in the three great representative institutions of Israel. The ‘Servant of the Lord’ in relation to Israel’s history was Kingship in Israel; the ‘Servant of the Lord’ in relation to Israel’s ritual ordinances was the Priesthood in Israel; the ‘Servant of the Lord’ in relation to prediction was the Prophetic order. But all sprang from the same fundamental idea: that of the ‘Servant of Jehovah.’
One step still remains. The Messiah and His history are not presented in the Old Testament as something separate from, or superadded to, Israel. The history, the institutions, and the predictions of Israel run up into Him. In this respect there is deep significance in the Jewish legend (frequently introduced; see, for example, Tanch. ii. 99 a; Deb. R. 1), that all the miracles which God had shown to Israel in the wilderness would be done again to redeemed Zion in the ‘latter days.’ He is the typical Israelite, nay, typical Israel itself – alike the crown, the completion, and the representative of Israel. He is the Son of God and the Servant of the Lord; but in that highest and only true sense, which had given its meaning to all the preparatory development. As He was ‘anointed’ to be the ‘Servant of the Lord,’ not with the typical oil, but by ‘the Spirit of Jehovah’ ‘upon’ Him, so was He also the ‘Son’ in a unique sense. His organic connection with Israel is marked by the designations ‘Seed of Abraham’ and ‘Son of David,’ while at the same time He was essentially, what Israel was subordinately and typically: ‘Thou art My Son – this day have I begotten Thee.’ Hence also, in strictest truthfulness, the Evangelist could apply to the Messiah what referred to Israel, and see it fulfilled in His history: ‘Out of Egypt have I called my Son.’ And this other correlate idea, of Israel as ‘the Servant of the Lord,’ is also fully concentrated in the Messiah as the Representative Israelite, so that the Book of Isaiah, as the series of predictions in which His picture is most fully outlined, might be summarised as that concerning ‘the Servant of Jehovah.’ Moreover, the Messiah, as Representative Israelite, combined in Himself as ‘the Servant of the Lord’ the threefold office of Prophet, Priest, and King, and joined together the two ideas of ‘Son’ and ‘Servant.’ And the final combination and full exhibition of these two ideas was the fulfillment of the typical mission of Israel, and the establishment of the Kingdom of God among men.