Get on that laser. It will probably work great for you (dark hair, light skin). But plan to be doing that for quite some time now. Electrolysis is much slower, more tedious, and expensive in the long run if you can get good results from laser.
Definitely let your hair grow out. You can probably do a lot with a better haircut. Also consider trying out some good shampoos. I've been using ridiculously expensive salon products and you know what? The work. Also, blow-drying makes your hair look much nicer, though long-term it can lead to some damage. Maybe you'll need transplants, but maybe you won't -- and see about getting on hair loss medication too. I doubt you'll need a wig.
Your face is clearly male, but I think that has to do mostly with the stubble and the hairline. Maybe your nose is a bit wide as seen from the front -- but it's very feminine for the side, as is your browline. Your chin isn't very prominent, which is usually one of the most difficult problems.
It might help to pluck those eyebrows -- in fact, consider waxing them (have it done by a professional) to get a more feminine shape; then you can keep them in shape by plucking. And you know what's really great about HRT? It really improves your complexion.
I hope it all goes better than you ever imagined!
