What is the best way to select the respondents?

The two most important factors are that they know the appraisee sufficiently well to be able to answer the questions with some degree of authority and that they will be honest. They should be people who the appraisee trusts and respects, they should be from a cross section of the people that the appraisee comes into contact with and they should not be under any pressure to mark in any particular way.