A CPU will make or break your new PC. An underpowered processor will not allow your computer to live up to it's full potential, with slow boot times, poor websurfing, and lackluster preformance in your favorite games. A properly sized processor will let your PC screem through everyday tasks, as well as the latest games.
When selecting a CPU, keep in mind the type of motherboard that you'll be using, as each processor and motherboard have a specific socket (or processor connection), and these change often. Just verify that each have the same connection.