No, printing Jesus' words in red doesn't make them more important than the rest of the Bible—and the reason is because all the Bible is God's Word, and we should take every part of it seriously. The Bible says, "All scripture is given by inspiration of God" (2 Timothy 3:16, KJV).
At the same time, whenever someone asks me where they ought to begin reading the Bible, I almost always reply, "Start by reading one of the Gospels." The reason is because Christ is the center of our faith, and the four Gospels tell us about His life, death and resurrection. But they don't just tell us what He did; they also record what He said, and His teachings are very important because they tell us how to live.
Most of all, the Gospels tell us who Jesus was: the divine Son of God, sent from heaven to save us from our sins. Jesus wasn't just a good person or a wise teacher; He was God in human flesh! And when we believe in Him and commit our lives to Him, He gives us the greatest privilege imaginable: We become His sons and daughters forever.
Make the Bible part of your life every day. Begin in one of the Gospels (I suggest you start with John), perhaps reading a few paragraphs every day. Ask God to speak to you as you read and apply it to your life. As the psalmist said, "Your word is a lamp to my feet and a light for my path" (Psalm 119:105).