I also like the idea of different subraces for the Giants just like we have with Elves, and to a lesser extent other races. I actually do enjoy a fair bit of the Forgotten Realms lore for Giants as being somewhat a perpetual second fiddle race to everyone else throughout their entire history. Even in the beginning they were getting bullied by Dragons which is obvious, while later on it was just how other races were just more pervasive.
I'm not terribly big on 'The Ordning' which classifies all Giants into a strict hierarchy but I do like the general concept of it, and that Giants see each other as kin, lesser or greater as it might be, but still kin with the same worship of the same deities and other cultural practices.
The common stereotype of the dumb giant brute giant can also be reflected by the DnD Hill Giant, or what we see reflected in Warhammer Fantasy with how those Giants eventually de-evolved into the Giants we see now thanks to competition to more successful (and while still big, still smaller species like Ogres) and those Giants eventually evolved into different subspecies as well with Forest Giants, Mountain Giants and Chaos Giants etc though all are pretty universally dumb-dumb.
But you also got smarter giants as well. It's not really explored much in the Game of Thrones show but the giants there seemed pretty smart despite oftentimes... not being so like in the final Battle of the Bastards with Wun-Wun or whatever his name was.
The sort of weapons used by the Giants would obviously have implication onto the type of Giant and who they are fighting on behalf of. Rocks, Tree Trunks and Barn Doors might be sufficiently terrifying to crush most medieval enemies but if you get smarter giants, you are right in that they can use terrifying bows with the range of hundreds of meters, be clad in armor, and use terrifying weapons like Scythes and Nine-Irons as mentioned prior.
In regards to the overheating problem, that could be a nice reasoning for why Hill Giants (besides their lack of intelligence) stomp around half naked. Meanwhile you have Frost Giants living in very cold climates and so can armor up, and Fire Giants are already overheated, hence the name, so they can forge away and needless to say, they are higher in stature as Giants go. Stone Giants, Cloud Giants and Storm Giants meanwhile, the latter two especially, don't really seem like the types to invest in petty mortal conflicts and have other pursuits. Plus tend to be even more advanced and use magic and the like.
One of the interesting things is bucking the stereotype of Giants being in the service of "Evil Races" because stupid people are attracted to evil. Which is still because as Spaceballs has intimated, it is actually "Good that is dumb." But more precisely, just because your dumb, doesn't mean that you are prone to evil.
In the Fables comics the exiled Fables, when they went to War with the evil Adversary and his Fantasy Empire, were able to enlist the aid of the Cloud Kingdoms (of Jack and the Beanstalk fame) and using diplomacy and respect and offering them advanced medicine were able to enlist the aid of the simple minded Giants in their War against the Adversary. Being less intelligent could just mean you are illiterate but thanks to your setting, you can still have a functional society despite it. Or being truly stupid doesn't mean evil. It just means you are innocent and you can be trained, influenced and raised to not be evil.
And if you don't want Giants to be traumatized by conflict, I'm sure that Giants, including the simple minded ones, can live very comfortable lives both in civilian life and in supporting war efforts since their size and physicality and strength can grant many benefits beyond stomping, clubbing and rock hurling.
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