Another thought if you can just save a bit up. I started my beard removal with a home IPL. No it's not the final answer but it did thin it out on my cheeks and neck. After months since I last used it, those areas remained thinned. For a little more up front there is a couple of home laser units. These may prove more effective and do not come with the replacement bulb costs. For what I spent on bulbs I could have bought a Tria laser unit and then some. On the plus side these units can continue to be used on other body hair. Like the breasts and chest. HRT help with a lot of it but I still have a bit that requires shaving. I was saving my bulb life for my face but after about 6 months of the IPL on my face I have given up. The remaining hairs need a professional laser.
Which leads to the next
step.you can shop around and find laser treatments priced per visit. This will let you get it done when you can save enough to do it. I know in the larger city there are some deals for several sessions for $100 while out in the rural area I have to pay around $300 each for a doctor or dermatologists nurse to blast my face.
One more thing, talk to the person before you sign on there. My first treatment the doctor running it left areas untreated. So after about three days without shaving I have circles of clean skin on my chin and jaw area. My next appointment is at a derm place and the nurse assured me she would not be so sloppy. She couldn't hardly believe so much got missed the first time I went somewhere.
Also I can actually recommend a battery powered home Electrolosis unit for scattered grey hairs. There is a unit branded Clean and Easy. It does work if you don't mind guiding a super thin wiring along your hair down to the root. I've found it takes 2-3 on cycles at 15 seconds each to really kill the hair. It is galvanic meaning the DC current reacts to produce lye in the pore. If you get it when you pull gently with a tweezer the hair and clear inner sheath will pull right out. The effectiveness actually seems to work better on my grey hairs. Not sure why, they just seem to take less lye to kill than the dark hairs do.
A small warning with this one. You need steady hands, a magnafying mirror, good light, and a gentle touch. If you jam the wire in you can poke yourself and cause a small blood scab to form from bleeding. If you are gentle you only get skin irritation a day or so from the lye in the pores. Also you can only kill the actively growing hairs, just like any other method. Also use rubbing alcohol to sterilize the wire and your skin surface unless you want a massive breakout.
This thing is only like $40 and a pair of replacement tips are under $10 for when you bend them, which you will.
Plucking and waxing do not work. You may end up with smooth skin for a week but it will all come back. I did it once. Glorious for a shot time to feel smooth skin on my face, but I want it to last.