Comfort level - Probably the most important factor is how you feel about the coach - the level of rapport or comfort between you. Does the coach appear to be genuinely interested in you? Do you feel you can trust the person with sensitive information? A poor connection will invariably undermine your development process, irrespective of tools and methodologies used by the coach. Ideally one needs an optimal level of identification between the two parties - comfortable but not too comfortable.
Experience and credentials - How long has the person been coaching? Since March 2004 I’ve logged more than 4730 hours of coaching and facilitation (as at June 2019). What kind of companies and people has the person worked with? What level of complexity can they work with? Generally a level of maturity or life experience combined with a solid academic qualification is a good start. We then need to also consider the person’s coaching related qualifications which can vary from short weekend courses to Doctoral degrees.
Full-time Professional or Part-time Coach - Does the person focus on coaching and people development full-time? A full-time professional coach will have significantly more hours of coaching experience - which adds to their overall level of competence in the field.
Location or convenience - Is the coach conveniently located and/or prepared to travel to a venue that suits you and your schedule?
Cost - Are fees based on 1 or 1½ hour sessions? Are you bound by an upfront payment contract or can you pay monthly after satisfactory completion of sessions? In my opinion large upfront payments are not a good idea for private clients. I believe that my clients should always have the freedom to immediately terminate their coaching process without any hassles if for any reason they change their minds.