Discuss with your institution its requirements for establishing a review committee. Be sure you understand how many reviewers the administration requires and who has the responsibility for finalizing the decision and inviting the reviewers.
Discuss with your department, or the departmental committee running the review, your criteria for diversity. Discuss ways of balancing gender, racial, and ethnic diversity with the diversity of fields, methodologies, and areas in your department. Since it is unlikely that there will be a reviewer for each subfield within a department, consider new ways of dividing the department so that your faculty will feel represented by the reviewers. For instance, in a department with subfields based on religious traditions, consider reviewers who represent both ethnographic and historical approaches, or broad chronological or geographical divisions. Best practices in hiring suggest the importance of articulating in writing the goals and criteria for a candidate so as to avoid the possibility that the search will run off track. The same is true for selecting reviewers.
Consider reviewers both from institutions similar to yours and from institutions or programs that you aspire to resemble. It helps to have reviewers who understand the particular issues at your type of institution, but also to have reviewers who can make useful suggestions to you and to your administration for how to improve.
Ask for nominations from your faculty, from respected colleagues at other institutions, and from the AAR. Don’t rely on your friends to be your reviewers; it is better to find people who are at an arm’s length, who will focus on the task at hand, and who will be willing to offer constructive suggestions.
Spend some time vetting your potential candidates. This should be done with discretion and confidentiality, as rumors can be false. Nonetheless, it is better to avoid asking someone because of unsubstantiated rumors of, say, sexual harassment than to discover after the invitation is tendered that these rumors are widespread and corroborated. Consider making a list of your top choices and your alternates by constructing a decision tree rather than a single ranked list of back-ups. That way, you can work to maintain your criteria for diversity as you move down your list of possibilities.