From my youth days I hardly recall reсipe of the black powder: charcoal, sulfur and nitrate. I was never curious what exact nitrate needed. But nowadays I see it can be: ammonuim nitrate, potassium nitrate, sodium nitrate… So, which one?
Check out the Everything Black Powder youtube channel. He makes his own black powder and tries a bunch of different ratios and components. He uses different carbon sources. He also tries ammonium nitrate and sodium nitrate instead of the usual potassium nitrate. Potassium nitrate is the safest and easiest to use. The other two are much more hydrophilic which can ruin the powder, in addition to being much more hazardous to have around. https://www.youtube.com/@Everythingblackpowder
I suppose I can’t speak out of practical experience but I do have some insight. For one, originally black power was made with what was called saltpeter, known now as potassium nitrate. That would be the “default” recipe. The other nitrates can be used but will likely significantly affect the burn rate of the powder. If you want to look into it, start with the standard potentials of each nitrate. Higher standard potential, stronger oxidizer, faster burn, more chamber pressure.
Any of them will work, it’s more what you can get ahold of cheap. I prefer to avoid ammonium nitrate personally. Not a fan of the smell more than anything.