The following discusses the ways often used in selecting systems. Actually, one area not expanded upon is the combination of an RFI/RFP combined with a Scripted Demonstration process.  Using the RFI to narrow the field and the Scripted business process to show the stakeholders how the system will function for them.
Sam Lowe’s blog on Enterprise Architecture & IT Strategy: Are Most Enterprise Technology Selection Exercises Flawed?
Are Most Enterprise Technology Selection Exercises Flawed?