i think sunrise's idea to speak to your school counselor is an excellent place to start.
here's a site that talks about therapy and the different kinds of therapies and therapists. it has a great question and answer section and many links to areas within the site to specific topics. i go there often and i like it very much:
www.guidetopsychology.com
it sounds like it will be hard for you to tell your parents and you're worried about their recation. choose a calm time, keep it simple, and emphasize that you are taking responsibility for finding a way to feel better and that you appreciate their help.
as far as finding someone you can 'click' with, it is something you have to try out by going for a few sessions. in that initial bit of getting to know one another process you'll see how it goes, how you feel about the therapist, how you feel in the presence of the therapist.
it's okay to not be sure about needing therapy. it's okay to go and talk a few times and see what it's like and if you like the therapist and feel comfortable ( you can feel nervous and anxious and also feel that the therapist is trustworthy and kind, someone you could talk to). that you want to talk to someone is also your need to talk to someone and good to act on. maybe you have some thoughts about 'deserving' therapy?
the therapist will have time for you. she/he will be very glad to make time for you!