Congrats on figuring out how to get the ball rolling!
In regards to your mom, from what I have heard you say about her at least, I would recommend tell her through a letter of some sort, since you'll be living elsewhere. From what I've heard, that also helps because she will have a chance to think about it since she won't have to immediately respond to you. It could make her response less strong since it won't be an immediate response. (COULD being the key word there).
If you let her find out on her own, she may be upset not only about your coming out, but also that you kept a secret from her, so I would be careful with that option. My mom would be mad if I kept a secret like that from her, but other moms may not care so much.