He persecuted the church of God and wasted it. Galatians 1:13 KJV. Why would the Lord choose him after that?
God's foreknowledge and wisdom
God knew Saul's heart, Saul was seeking to serve God, but was in error in how to do it, much like popular Christianity today.
Romans 8:29
For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren.
30 Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.
2 Timothy 1:9
Who hath saved us, and called us with an holy calling, not according to our works, but according to his own purpose and grace, which was given us in Christ Jesus before the world began,
Ephesians 2:10
God foreknows the response of people when they are presented with truth.
Saul simply had not heard enough truth to believe yet. or rather accurate truth.
God is the searcher of hearts.
He looks on the heart, not the outward appearance.
He knows what you will have for breakfast tomorrow and your every thought all day long. He already knows how you will choose to respond to this post, whether you ignore or just read it or reply to it....
He foreknows if you will have digestive problems next week or not.
He foreknows it all. He wisely chooses based on that foreknowledge.
The ones He foreknows will believe, he elects, he chooses for his own.
He sees past our errors for he sees our righteousness he gave us.
He looked past Saul's errors and chose him for many reasons, Saul was a faithful man to what he believed, and when he learned that Jesus is the Christ, not a heretic, he was faithful to that truth.
Was Jesus a heretic? The contemporary religious elite thought so.