How Do You Choose a WAN Carrier & Technology?

Giger51 asks: "I'm trying to get a better idea of how a business goes about choosing a carrier & technology for their Wide Area Network. For the last little while, it's been difficult for a lot of the carriers out there. Those difficulties have resulted in questionable accounting practices and bankruptcies. When trying to make the decision, what are the key points that are considered? What technology (IP, Frame Relay, ATM...) are you avoiding or looking for?"