The correct order has three tiers.
Accreditation. The right to practise, training in a recognised method, and supervision. These are checkable and not negotiable. A profile that does not say what training the person has is a reason to ask directly.
Fit with the problem. A therapist who is excellent with anxiety may never have worked with grief or eating disorders. It is a legitimate question and offends nobody: “have you worked with situations like mine?”
The therapeutic alliance. This is the part people underestimate. Meta-analyses consistently show that the relationship explains a larger share of outcome variance than the method used. In practice: it matters whether you feel heard, whether you can disagree without fear, whether you have a sense of working together rather than having something administered to you.
Worth testing in the first sessions: do you feel safe saying something uncomfortable? When you disagree, what happens? Did you leave feeling understood, even if nothing was solved?
A poor fit is not a failure and is nobody's fault. A good therapist does not take offence when you say it is not working — often they will recommend someone. If after three or four sessions it feels like talking to a wall, that is information, not proof that therapy is not for you.