I am very much a DIY'er and doing my own HVAC repairs have never been out of the question. Actually, I have rebuilt a couple of systems, less the pressurized parts of the system.
HVACs are great until they aren't and the need for repairs always comes up at the worst possible time. It would be nice to know more details for those reasons.
If you ignore the direct question about charging an HVAC, there could actually be a small, slow leak in my system as it stands. That'll get troubleshot in due time. (Still, I don't think I have ever had a system that didn't need the system to be topped off after a few years, even with no detectable leaks...)
It doesn't seem difficult: Ensure system is at correct temperature; attach a gauge; depressurize/pressurize as needed.
There has to be some "gotchas" in there somewhere. The equipment is cheap enough and I am fairly sure I can source the correct refrigerant easy enough.
Aside from needing to store and manage a small supply of refrigerant and that there are some annoying risks (like a system freezing over, etc..), what cost factor and equipment am I not taking into account?
Not a professional but Ive DIYed it. So the following may be oversimplified and/or not best practice.
You'll need a gauge set so you can watch both the high and low side pressures. Your unit probably does not have ports to attach the gauges but they make some adapters that bolt on and pierce the lines. These work ok but will probably be another spot for leaks down the road.
You'll need to figure out what refrigerant your unit has in it, there's usually a metal placard somewhere that tells you this. This is how you'll look up where your pressures need to be.
Finally you'll need to source said refrigerant, which you likely cannot buy without a license or bribing someone.
The actual charging procedure I would look around on youtube for. It may vary depending on your type of unit but it's usually pretty straightforward.
Does this apply to heat pumps?
I have no experience whatsoever with heat pumps. I think they do some black magic with reversing the refrigerant flow; so there is probably a whole other set of specs and procedures for those.
If the concept of a reversing valve is wholly alien to you, I cannot recommend you DIY your issue. Just hire someone, it goes beyond convenience or annoying risks, it's your safety that I'm questioning. Frostbite, electrical shock, poisoning, risk of explosion, severe burns, suffocation, there are so many ways that trained techs get hurt or killed when they don't respect the safety element. No way in hell am I going to tell a stranger on the internet to take that risk for themself or someone around them.
Please just hire someone.
Edit: just realized you're not the OP. Still gonna leave this up. This kind of work is simply not suited to being done by non-professionals.