[SteamBub]

I'm just going to throw some thoughts out.

For a government backed entity, in the United States, I would imagine that it was founded before or after the independence from Britain. The early colonist should have been dealing with the beasts of the woods, Wendigo, Flying Heads, Black Dogs, and malevolent fair folk. So the people would organize hunts and a veteran from hunting might go around helping other communities. This would go on unwritten, or at least not as official, as who would believe monsters was the reason they couldn't meet export quotas? Then one day some of the founding fathers were saved by some volunteer hunters, which kick started the building of an official monster hunting agency.

For the group above, they might hide and be funded by a cover agency. Something along the lines of the Federal Wildlife and Game something or an other. Equipment would just be decommissioned items from military or other government agencies. Since this group is off the books the items wouldn't have to follow the modernization quotas set by law.

For monsters that hide among humans, I can guess Big Brother would be keeping a close eye one those. And moles would be out and about, better alive than dead helping some mysterious folk.

Funding independent hunters would be easy, just have a job. Rifle, pistol, and gun collecting is a hobby for some in the states and you can easily buy weapons that would be effective against monsters. And very legal in many states. Other ways might just have a front. The on the book government bodies might list these fronts as cults, secluded communities, terrorist groups, or anything that may show up on a FBI watch list. Or maybe independent hunters are just organized crime members. They act morally questionable in human society, but are the first line defense for humanity in the underworld.

Keeping out of trouble may be a little harder I would guess. Independent hunters may act more like hitmen than anything else. Try to make everything look like an accident or if guns need to be involved, plan the ins and outs as much as humanly possible. If caught, just need to try to make sure the monster parts are not found out and just bite the bullet for humanity.