Hi Aelita_Lynn,
I would recommend the letter or email approach for coming out. It would give you a chance to get your thoughts down how you want them to, without the possibility of getting distracted from the conversation, which could be most awkward indeed. Just tell flat out how you feel and what goes on in your life, and why you need to do this for yourself.
And the fear is completely understandable

, a lot of us have been there and done that, so you have a ton of people backing you up in how you feel. I remember my first coming out with an SO, I don't remember exactly, but I do know I never knew clicking a mouse button on "send" could ever be such a difficult thing to do.
It sounds like your parents are open-minded from the way you speak about them, so it sounds like it will turn out well. I wish you the best of luck on this

.