Samuel anointed David king of Israel due to Saul's disobedience (see 1 Samuel 15). Prior to anointing Saul as the first king of Israel, Samuel rebuked the Israelites for wanting a human king like the surrounding peoples, instead of being content with having the LORD as their king (see 1 Samuel 8). Without a doubt there is a lot going on in all this both historically and politically. It is rather Shakesperian.
This prophetic outburst of Samuel highlights a tension in ancient Israel, one that is best brought into relief by reading 1-2 Samuel and 1-2 Kings- 4 installments of the same history- over and against 1-2 Chronicles. The work of Margaret Baker is most valuable in this regard. A great starting point is her short book Temple Theology: An Introduction.
King Saul was a member of the tribe of Benjamin (1 Samuel 9:1). Much later God would call another Benjaminite named Saul, better known as Paul, which was likely his Roman name, as apostle to Gentiles (Phil 3:5).