The puzzles of the Myst universe (at least for the first few) were generally mechanical in nature and usually had hints scattered around the world. So, not only did you have to find the hint, but you had to realize what you were looking at, and put everything together. (I have vague memories of one puzzle where there were these orbs with scratches and numbers on them. You had to assemble the conversions then realize that you're doing equations in base-7 or something like that, to solve it.) Some of the earlier ones had levers and buttons that clunked... and nothing. Forcing you to hunt around for exactly what changed when you did that. That got pared down.
The original Myst had effectively had one inventory item-- book pages. They were the final objective of each area, and used to get the hint to open the ending. Latter ones got a feeeew more items, but they're all storyline driven, not puzzle-based.
In terms of an explicit story, there was some, but I'd say it paled in comparison to the worlds. A lot of it came from the atmosphere, looking at what was in each world, and trying to understand what happened from what's left. (Think anthropological.)
I found the later ones to have less obtuse puzzles. They were... a bit more standalone? Instead of hunting around for scribbles on a wall that corresponded to musical notes that you had to map onto a breaker (a bit of a stretch for what you might have actually seen, but not THAT much...), you might end up with something like having to use switches to turn on the correct lights to navigate a tunnel.
(If you're looking for something more in the vein of King's Quest/Monkey Island style adventure games, you might take a look at Daedelic Entertainment's stuff. Love the Edna & Harvey series, though they're a bit rough around the edges. And have some of the most unreliable narrators ever, though that's intentional.)