a resident of Lystra, a city in the province of Galatia (Acts 16:1-3). He was the son of a Greek father (Acts 16:2) and a Jewish mother named Eunice (2 Timothy 2:5). From his youth he was taught in the Scriptures by his mother and grandmother (2 Timothy 1:5; 3:15).Those are the general facts about who Paul was writing to. Timothy was a young man who loved God. He was in Paul's words "a true son of the faith".
Paul wrote to Timothy to help him in his charge of leading the Ephesian church. There was much for both Timothy and Ephesians to learn so Paul set out to help them (empowered of God to do so).
I am imagining that reading through these letters that they will be filled with practical advice on how churches and Christians should operate as believers. And my initial reading confirms that. From Chapter four we get these words of wisdom:
Rather train yourself for godliness; 8for while bodily training is of some value, godliness is of value in every way, as it holds promise for the present life and also for the life to come. 9The saying is trustworthy and deserving of full acceptance. 10For to this end we toil and strive, because we have our hope set on the living God, who is the Savior of all people, especially of those who believe.