What are key things to look out for when choosing a private assessment?

Is there like a checklist on what to look for / what not to fall for? I've mostly been considering:

- cost of assessment

- additional costs for all the rest

- is it a psychologist or psychiatrist? The latter can prescribe medication.

- will my GP recognize their assessment?

- what are the wait times?

- will they do face to face or online?

Thanks guys!