Hi, welcome! It's a little weird to be dishing out welcomes, since I'm a newbie myself, lol.
I'm kind of like the least qualified person to be giving advice, but I'm going by my own experiences and what I've personally done.
Well if you're making progress with your voice, that's good. Keep doing plenty of that, because it will help you pass as you get better. Establish a support system. Friends, a confidant, whatever. Having people to talk to lowers the stress and tension in your life dramatically. This is important because a better state of mind makes for an easier transition.
For facial hair, you're going to generally want to go with electrolysis. When the electrologist kills the follicle, if it's done right, the hair's gone for good. It's also not as painful as laser. Laser hair removal is also an option, but is more expensive in the long run and needs to be maintained as it isn't permanent. It also hurts a lot. I had it done and it didn't really work for me personally, but YMMV.
As far as talking to a specialist, that really depends on you and what you want. There's not really any "when", just what feels right for you, but the changes made by hormones may help you pass easier. Just keep in mind that every physician is different. Some will give you hormones right away, while others might want you to make a few appointments with a therapist prior to writing up a prescription. Some may also want to start you on AAs to kill the T before adding the estrogen.
And keep in mind, it's a slow process. Don't expect everything to magically change overnight. The changes induced by HRT may take up to several years to reach their full effect.