My plan was to do 4-12 lasers and use electrolysis to finish up what the laser can't remove.
My technician and information on the internet says the ideal patient for laser is dark hair with a light skin complexion. I am very very fair skinned (I use 0.5 color in Urban Decay foundation) with medium-dark brown hair color there. Prior to starting a had a very thick facial hair.
I am currently on session 4 and started HRT about a bit before so I really can't definitively tell you what has had an exact affect. So the first session was by far the most painful and hurt the most. but on the plus side once the redness subsided it seemed to have a pretty large affect on the amount of hair growth. Each session after that got less painful but also less change. after the third session I noticed a substantial drop in dark hair growing back on my face. the only hairs after 4 sessions that seem to grow back are, as expected, blonde and red. my growth patterns are odd, growing in an almost streak like pattern.
The one interaction in this process I noticed was how translucent my skin has actually become. I noticed that hair growing under the skin (especially on my upper lip) has become more noticeable however it is quite easy to cover up with concealer/foundation and doesn't give me much problems after that.
I didn't buy the package so my sessions cost 350$ each if that helps. and no hrt as said by everyone else doesn't have an effect on facial hair, some cis women develop facial hair as well and use the same process to get rid of it

I had the same question about starting but what my tech said was that starting laser asap is better because while HRT doesn't change growth of the hair, it can change lessen the pigmentation of the hairs, making it harder to remove with laser. I don't know how true this is for facial hair, but hair elsewhere seems to be effected.
to be clear I still have to shave with laser, but its almost exclusively red/blonde hairs which is to be expected. Hair removal really does suck but its just one of those things we have to go through if we want it gone.