Stephen, typically you want to appraise a property for the purpose of some kind of financing. I have always approached things from the other direction.
Talked to my Mortgage Broker first, determined who we are going to use for financing (i.e. which banks). Then have my mortgage broker recommend a list of appraisers that are on the `banks approved list`. Once I had this list I phoned a couple, had a brief conversation with them, surveyed their knowledge of the area I`m looking at, then picked one that sounded like they were an expert in that area.
As well, I always like to write a cover letter to my appraiser coming to appraise the property, and in that cover letter you can sell the details and state your case of what you feel the property is valued at... (I bet you have a good idea right now). You would be surprised how close your are, and how much of the information you include in your cover letter makes its way on to the appraisal report. In essence you are helping them with their job, almost like you do when you complete your sophisticated investment binder for your mortgage broker.
Bottom line, make sure the appraiser is on the banks list, so you do not go through the time, effort and expense of completing an appraisal only to hear from your bank, "thanks for the appraisal, but that company is not on our list. We will have complete a new appraisal with someone from this list" ... Guess how I learned that one
Cheers