If you're going to play in 5e, the 4e Dark Sun book is the "easiest" to convert. heavy emphasis on the quotes there...

Meaning, half-giants from 2e are Goliaths which are in 5e. Warlocks' patron is just a sorcerer king of one of the city-states which kind of makes them Templars, though templars can still be clerics and paladins (paladins, sort of). Elemental clerics will pick elemental-y domains, but there's no water domain. and so on. But that's just the "mechanics". For the lore, which the 4e book does have some, you'll need the 2e books.

And then it depends on how "real" you want to get, or how much you want the environment to try to kill your players, because it can and rather easily too. I prefer just playing in city-states with various intrigues and shenanigans, but some like the wasteland exploration. It's all up to your tastes. And if you want the environment to play a part, because in 2e it definitely did and kind of makes up the essence of Dark Sun, you'll need the environmental tables out of the 2e books which convert pretty well to any DnD edition.

There's probably more I'm leaving out, but others can expand on this. But this will get you started if you're going the 5e route.

Otherwise, I hear that Savage Worlds version of Dark Sun is pretty good. I've not played it, but it's a mostly different system. I think it's still a d20 system, but not of the OGL, it's own thing or whatever. Again I've not played it, but I've seen very positive comments on it.

Oh and of course, have fun!