Look at their ratings from customers, BBB ratings, and read payment processor reviews. There are some companies that have gotten reputations for hidden fees and bad customer service that you'll want to avoid.
Beyond that, see that they fit your business. Some companies are better for smaller ticket sales, others for mobile or online payments. Some are better for high-risk transactions or high ticket sales. It's difficult to name just one best credit card processing company for small businesses with so many variables.