As a psychologist, I would strongly recommend against anything related to skype. This is not an appropriate venue for a child. I agree with several others here that you need to trust your instincts with the first visit or two. If possible try to avoid relying on insurance. Many plans allow you to submit for out-of-network coverage, but there are many highly qualified therapists who refuse to accept contracts with insurance companies because of reduced confidentiality, as well as extremely reduced reimbursement. And your pediatrician, school counselor, minister/priest/rabbi may be good referral sources.

I have written about therapy in several blog posts; I hope some of these might be helpful:

http://giftedchallenges.blogspot.com/2016/01/five-misconceptions-about-therapists.html

http://giftedchallenges.blogspot.com/2015/10/gifted-children-and-adults-when-is.html

http://giftedchallenges.blogspot.com/2013/11/when-does-therapy-benefit-gifted.html