Generally for an appraisal, if it's your insurance company requesting it, they will provide* a few companies/people who's reports are acceptable to them. Using a "preferred appraiser" can save you some hassle.
*Your broker/agent/bank/insurance company can't offer the referrals without you requesting it as you are entitled to select whoever you wish to appraise your vehicle. However, the insurer reserves the right to decline an appraisal that lacks sufficient detail.
When an appraisal has been requested, clarify exactly what they are looking for. Sometimes they are only looking for an educated opinion of the replacement value of a vehicle which can be a simple 1 page report with very little detail, other times it can be a much more in depth, "vehicle condition and equipment assessment" which is several pages and contains multiple pictures. Obviously you will pay more for the more detailed appraisal, so make sure you aren't paying for an insufficient report or more than you need.