To prepare for coming out to my parents, I wrote them letters. Pages and pages of letters that I never intended to hand over to them. It helped me work out what I was feeling, what I needed to say, and how I needed to say it. I recommend it to anyone coming out, because writing can organize and cohere your thoughts in a way other mediums cannot.
I built a coalition of the willing. I found folks that I was really close to, and who I had a notion would be accepting, and I told them first. They weren't just low hanging fruit, they were an alliance I could call upon if things came apart down the road. I recommend the same. Find people who you trust, both in the department of discretion and the department of acceptance, and bring them on board. Have them on hand when things grow more difficult.
I chose my moments and my methods. There are lots of good times to come out, and there are lots of bad times to come out. Working with that in mind, try to find the good times for each person you come out to. It's a stressful event for all involved, and the less external stress, the better.
Stick to your guns. Of all the advise, this is probably the most important. You can't afford to let other people's doubts control your transition. Your motives may be impugned, pleas for proceeding slowly my come up, the entire notion that you're trans may come into question. You know you, you know how you want to proceed, and go in with that firmly in mind. If someone has good advice, take it, but don't let anyone take control. Coming out is not a negotiation, it's a declaration of intention.
Finally, you're right... people are going to be hurt and stressed. It's impossible for it to happen otherwise. So many relationships that require a coming out are based on gendered relationships: father, daughter, husband, wife, niece. Those people are going to be in pain. You can't avoid or prevent that, even if you live the rest of your life in the closet. You'll cause them pain with your pain, and you'll cause them pain by depriving them of the relationship with the real you. The pain of coming out is, in many cases, temporary and useful pain. The other kind? It's pointless.
I was where you were, just a few months ago, and I did it. It was, honestly, the best thing I've done. Nothing beats the joy of living authentically. Even if you can't come out everywhere, you owe it to yourself and your loved ones, to come out in the places where you can.