There are numerous types of handle bars. Made from rubber, foam, leather, cork, you name it. The choice is yours. But what is most important is how they actually feel. So it pays out to go to a bikeshop where you can test several types.
When testing it's important how they feel. Ask yourself the question: "Will I have sour hands after a day's use? Will my hands getting tired quickly? Can I chance my hands in several positions during cycling?"
Last, but not least, the handle bars have to look good. Solid. Thorough. Reliable. Logical. Giving good grip.