Assuming you’ve already played the story of the expansion, I would personally start with the lore books. They give the biggest chunks of lore and set up some important story beats that other lore follow.
Armor and weapons with lore tabs are good follow-ups, usually more self-contained stories or teasers for what’s coming up next.
You can go to the Releases page on the site to see it broken down into categories that make it a bit easier. Check out the Records tab when you’re in there because that’s where the web lore gets put and that has a lot of context too.
So in short I’d say my main preference would be: main story → --> Records (if there were any for that season) → lore books → weapon/armor sets → maybe peruse the season’s general interactions/items if you want every single tidbit
I also can’t suggest Previously On Destiny enough if you’re looking for quick recaps of anything you think you’ve missed.