Heart of David
In appointing someone to replace King Saul, God, through the prophet tells Saul the following, “But as it is, your kingship will not be established. ADONAI has sought for himself a man after his own heart, and ADONAI has appointed him to be prince over his people, because you did not observe what ADONAI ordered you to do." (1Sa 13:14, CJB)
God then reaffirms to the prophet Samuel, that David’s heart it right before God.
But ADONAI said to Sh'mu'el, "Don't pay attention to how he [Saul] looks or how tall he is, because I have rejected him. ADONAI doesn't see the way humans see - humans look at the outward appearance, but ADONAI looks at the heart." (1Sa 16:7, CJB)
This is further confirmed by Paul in the New Testament.
God removed him and raised up David as king for them, making his approval known with these words, 'I found David Ben-Yishai to be a man after my own heart; he will do everything I want.' (Act 13:22, CJB)
Prophecies of David
2 Samuel 7:12-13 tells how that through the line of David, God will establish His Kingdom forever.
One thousand years before His birth, David’s Psalms describe in detail how Yeshua will die and then also rise again. Reading Psalm 22 and comparing it with the historic account of the crucifixion in the New Testament speaks for itself; while Psalm 110 goes on to speak of Yeshua’s future reign and judgment.
In keeping with his promise, God has brought to Isra'el from this man's descendants a deliverer, Yeshua. (Act 13:22, CJB). The complete genealogy can be found in Matthew 1
In David we see the grace of God i.e. even though we make mistakes (David committed adultery and murder) God is willing to forgive us if we, with a broken and humble heart, confess and repent (Psa 51; this psalm really captures the heart of David and his relationship with God).
David said to Nathan, "I have sinned against ADONAI." Nathan said to David, "ADONAI also has taken away your sin. You will not die. However, because by this act you have so greatly blasphemed ADONAI, the child born to you must die." (1 Sam 12:13-14, CJB). However unlike David, because of his descendant, Yeshua (Matt 1:16), we no longer need to fear death for our sins. As an aside, Matthew (Matt 1:1-16) follows the line of Joseph [Yeshua’s legal father], through David’s son Solomon, while Luke (Luke 3:23-38) follows the line of Mary [Yeshua’s blood relative], through David’s son Nathan. We therefore see that David is an important link in the chain to the coming Messiah.
A final interesting point is that the Hebrew consonants for David's name are "D", "V". "D" = DaViD and these add up to "14". Hence Matthew arranges his genealogy in 3 x groups of 14, making it easier to pass this information on to succeeding generations.
In short, David a man after God’s own heart is both an example to, and an encouragement for all those seeking to have a personal relationship with God. In his flesh, David lived a less than perfect life but in the spirit he hungered and followed after God (Just as a deer longs for running streams, God, I long for you. I am thirsty for God, for the living God! When can I come and appear before God?; Psa 42:1-2, CJB). Through him comes the Messianic line that ultimately brings us Yeshua and with Him the possibility of eternal life to both Jew and Gentile (John 3:16).
King David is a great example and encouragement for the Disciples of Yeshua.