The Storyteller system is a good general system if you're looking for a dangerous post apocalyptic survival setting. The Chronicles of Darkness rulebook has base rules that would be well suited for building characters that excel in non-combat roles, and the health system makes combat super lethal (your average human is not surviving more than a few bullets, blows from a skilled swordsman, or getting hit with a semi-truck). Plus you've got a few ready made enemies good to go just by throwing a template on something, or knowing a basic dice pool for a construct. The World of Darkness - Shards book has setting hacks for a post apocalyptic world and a fantasy medieval one, and a few definitions of the scale of a disaster, depending on how far you want to lean into stuff. It's also compatable with Chronicles for the most part. The downside is you're going to have to look around a few more splatbooks than just the core to really get the most out of it. Creating a 'racial' system could also be a bit of a problem as Chronicles was designed with a humans only modern setting in mind. It's versatile though, and the system is easy enough to get an idea of as it's a dice pool. Each number of a stat represents a die you put in the pool for a roll. Attribute + skill = dice, count successes.
Warhammer Fantasy Roleplay might be a better choice. It has an unforgiving health system (though with a lot more wiggle room than Chronicles of Darkness), a variety of career paths and rules, weapons, plenty of source books to draw off of, and a variety of skills that can encourage non-combat solutions to problems. That being said, Warhammer Fantasy does lean heavily on the setting of Warhammer Fantasy (what a shock) so you'll have to refluff a variety of things. The upside with WHFRP is you've got stuff for demons, wizards, fantasy races, and crazy mutants poisoned by magical background radiation built into the base game and a few other splatbooks. The downside is all of it is tied to a well established world, and you might need to work a bit harder to file off the serial numbers and edges than you'd like. what also might be a bit of a problem is getting used to the success/failure levels of your average character. WHFRP uses D100 as its base system, so it's all percentage based rolls and that can mean encounters that do drag on a bit. But it also means that when you succeed hard, you really succeed hard. The critical hit effect tables are pretty brutal too.
Otherwise, you could use GURPs, or see if there's a 5e port for Dark Sun and look for setting rules for it. 3.5 has a lot of material, yes, but do also note that 3.5e is even WORSE than 5th ed at creating high fantasy hack and slash. Casters are extremely overpowered. You seem to be aiming for a roleplay rather than a roll-play style of game, and while 3.5 can provide that, it's harder for newer players and GM's to keep it from turning into that roll-play chasing the next +1 sword. Pathfinder fixes a few of the problems of 3.5e and then adds in its own problems. Pathfinder is 'better' than 3.5e from a pure mechanical standpoint but doesn't fix any of the core issues of 3.5e.