Hebrews 12:1-3 could be preached as a conclusion to a series of sermons on the people of faith in Hebrews 11.
If you use the lectionary, Hebrews 12:1-3 is one of the readings for the Wednesday of Holy Week.
If you are a pastor in the Dutch Reformed tradition, and your text selection is guided by the content of the Heidelberg Catechism, Hebrews 12:1-3 could be preached in connection with Answer 115, where the Catechism speaks of how we are to “never stop striving, and never stop praying to God for the grace of the Holy Spirit, to be renewed more and more after God’s image, until after this life we reach our goal: perfection.”[1]
On the question of what the limits of the text should be, see the review of where the text begins and ends in Hebrews 12:1-3 – Step Two.