Answer Given: Paul said that he was a minister of the new covenant. Since he was responsible to preach the new covenant, I think it is compelling for us to herald the new covenant, too. What we find then is that we must primarily preach Christ and herald the new covenant, which is New Testament literature, the mystery now unfolded that was hidden in the past.
At the same time, we draw on the illustrative material in the Old Testament. I think the Old Testament material can be summed up like this: First, it describes God. Then, it gives His law for life, His rules for righteous behavior. Third, it shows how God blesses those who obey, and fourth, how God punishes those who don't. The Old Testament also becomes the great source of illustrative material as we reach back to get some of the magnificence and fullness of God before the cross.
Another personal component for me is that when I was in seminary I realized that I could not be expert in Greek and Hebrew at the same time. Having had twenty-four units of Greek in college, I decided to follow that up and pursue New Testament studies as a primary objective for my own life and ministry.
The third little piece for me is that I have a personal goal in my life to preach through the whole New Testament. I desire to herald faithfully all the counsel of God and the revealed mystery of the new covenant. Occasionally, for variety I will sprinkle in an Old Testament series such as a study of Genesis or Daniel, or a character study.
My Note: Paul also said, “For whatever was written in former days was written for our instruction, that through endurance and through the encouragement of the Scriptures we might have hope” (Rom. 15:4).