I'll just make this one point. (There are too many thirty minute sermons that could be a part of this post.)
4 Against you, you only, have I sinned and done what is evil in your sight, so that you are proved right when you speak and justified when you judge.
We think of our sins as being against another person or from breaking a law or just doing something bad. But David knew that ultimately sin is against God. God is the one who has said what is sin and He is the One that said the wages of sin is death.
The cool part is He is the One that paid that price. But the gift of God is eternal life through Jesus Christ our Lord.
There are many other beautiful truths in this Psalm. I'm sure you saw many of them.