To me, an interesting case to consider is the rock attack used by giants. Now I know that PCs operate under a slightly different set of assumptions from NPCs, but taking the Hill Giant as an example, it's clear this is a Ranged Weapon Attack that uses Strength. It's also clear the Hill Giant is proficient with rocks, which is not surprising considering that monsters are generally assumed to be proficient with their attacks. Theoretically, it could be the Hill Giant is proficient with improvised weapons, but I don't think that's what's going on here. Rather, it seems to me the rock is a weapon with which proficiency is available to Hill Giants, but is it a melee weapon or a ranged weapon?
The use of Strength would suggest the rock is a melee weapon with the thrown property, but no melee attack is listed for it. It could be that Hill Giants simply prefer their greatclubs for melee, saving their rocks for foes at range, but I don't think so.
I think rather that the rock is a ranged weapon with the finesse property, similar to the dart used by PCs. Hill Giants use Strength because they'd rather have +8 to hit and do 21 points of damage than have +2 to hit and do 15 points of damage (or the fictional equivalent).
If a PC were to pick up a suitably sized rock and throw it in imitation of the Hill Giants how would you adjudicate it?
Personally, I would start with the fact that for the PC proficiency with rocks is unavailable without a feat, so no proficiency bonus would apply. Secondly, I'd give the rock the finesse property so the PC could use a choice of Strength or Dex. Thirdly, the rock would do 1d10 bludgeoning, the damage of the Hill Giant's attack scaled down for a medium creature, 1d8 if the PC is small.