2e Dark Sun was my first introduction into D&D. My first ever D&D game started me out in a tavern in Tyr.
I played for several months before I started reading the novels. My DM ran the published adventures the whole time. I never once noticed something in game that I thought should not be that way due to events in the novels. So obviously what happens in novels doesn't have to affect your current game. I don't think it would be difficult to do a little tweaking to an adventure so it fits in the time frame you want to run your world in. I've never understood peoples complaints about a novel affecting their RPG game
Oddly enough, I have always given credit to the novels for helping me be a better player in the Dark Sun campaign.
Once I started reading the Prism Pentad series, I gained a way better understanding of the setting, the cities, and the natives. I was able to roleplay my PC so he fit in the setting much better than he did before I read the books. It made playing in the setting a lot more fun for me.
I thought all of the Dark Sun novels were interesting and worth reading. Sorak from the Tribe of One series has always been one of my favorite characters from any D&D novels. I think he is
way more interesting than either Drizzt or Raistlin.
The Chronicles of Athas series was my least favorite series, but I still thought they were good books. You sorta need to have an understanding for how templars are before you read that series so you can relate more with the main character. So I'd read this series last, or read it after you've interacted with Athasian templars a few times in game.
I'd suggest reading the Prism Pentad series first to get a good idea for what the setting is like. Then I'd read the Tribe of One series next just because I thought it was a cool series. Then I'd read the Chronicles of Athas series if interested, it's worth the read and it's thought provoking.
All of the books will give you a better idea for what the Dark Sun setting is like.