Samuel had to anoint a king because the people asked him to so he picked Saul to be the king.
Saul disobeyed god and tried to kill David out of jealousy for him for the battles David one and the songs that were written for him.
Saul died against the battle of the Philistines then David became king in his place. when David was king he united Israelite tribes and one the battle against the Philistines.
David wrote the bibles book of psalms and David had a son Solomon and he became the next Israelite king after David.
when Solomon became king he built a temple it was the first temple in Jerusalem he also brought with him a long period of peace and built more cites then just the temple.
Solomon wrote the book of proverbs in the bible but people were starting to get tired of his little building projects and turned against him then everything including the kingdoms were divide and seprated