There are a several factors that should be considered when choosing an auditor. I have grouped these under three broad headings: Capability, Strategy and Cost.
Capability
Size of audit firm: Larger audit firms are often able to offer greater depth of experience and a larger pool of resources to draw upon, but that may come at a higher price than a smaller firm.
Related experience: you will likely want to know that the audit firm has experience working with clients in your sector. For example, if you are a not-for-profit organization then you may want to ensure that the assigned audit team has conducted audits of NPO clients that are similar to you.
Staff continuity: A significant amount of time can be spent initially training auditors on your specific processes and procedures. As far as practically possible, the audit firm should strive to keep the same staff assigned to your account in subsequent years, to avoid the time and cost that this retraining imposes on you and your staff.
Quality control program: Many audit firms have developed their own comprehensive quality assurance processes, that include training programs for audit staff, and documented systems and processes which they use to conduct their audits. One question you may wish to ask is whether there are multiple levels of review of the audit work.
Strategy
Audit strategies and methodologies: There are a number of different approaches to conducting an audit, and it is helpful to understand the differences between each when evaluating audit proposals. These may include for example substantive or risk-based approaches, and value-added approaches focussed on identifying improvement opportunities.
Time to completion: If you must have the audit completed within a certain period of time following year-end, or if the final report needs to be ready by a specific date each year, then the audit firm must be able to accommodate these requests in its work plan.
Team mix: In audit firms large enough to have audit partners, senior auditors, and junior staff, it is important to know approximately how many hours will be spent on the audit engagement by each level of person. If there is little involvement of the partner, then the experience and expertise of the other staff becomes of greater interest and importance.
Cost
Audit firms are often engaged for a multi-year period, with annual audit fees set at a fixed amount, or to be increased by a specified amount (for example the rate of inflation) over that period.
The quoted audit fees will usually depend on you providing the auditor with required audit documentation, supporting working papers and the preparation of year-end financial statements. It would also assume that there would not be numerous audit adjustments, and that there would be no significant change in the size and scope of your operations.
By keeping these criteria in mind, you should be able to successfully find the auditor that best meets your needs