I agree, it's very natural to be scared.
I recently came out to my Mum (Have yet to tell Dad) and have to say it was the best thing I have ever done. Very hard to do, but totally 100% worth it.
I told a friend, who I am close to and trusted very much first. She helped me a lot, someone to talk, someone who didn't judge me.
Ultimately it's about how you feel comfortable, and who you feel comfortable telling.
I wanted to tell my parents, but was scared, I fully admit. Then an online friend said something when I told them I was scared to tell. They said:
"But that will not change though, no matter how long you'll wait. "
Which made me realise, I just had to tell one day. A couple of days later I left a note to my Mum saying I wanted a chat some time soon in private, and came out in that chat with her.
I wish you the greatest luck, and remember, your parents will love you no matter what. Never be ashamed of who you are, and never be scared to admit your sexuality. It's a part of you. If anyone has a problem with your sexuality it's their problem, not yours.