A decade ago, I went to my dermatologist and asked for help with facial hair removal. The response I got was getting laughed at, and then he said "that's not dermatology, it's cosmetic". So my first recommendation is make sure you explain that you're trans to any doctor or professional you encounter for facial hair removal.
If you want permanent results with maximum efficacy, definitely do electrolysis. If your hair is especially stubborn, you should start HRT first to get your hair to change to a more cooperative state before getting the electrolysis.