I tend to 'over-answer' things, but here goes:
Story:
I would like to see a tie with other games in the series, but I don't know if it matters how/where the story links. Any story needs to be self contained and interesting. So any link to the KF sagas is secondary to making characters and happenings that are compelling by themselves.
Gameplay:
Exploration, danger, sense of isolation, dreary setting. Combat that requires you to adapt your technique/equipment to the current enemies. I would rather have less equipment, where each piece served a unique function rather than tons of stuff where new pieces kept outdating the old.
Puzzles/secrets are nice, but I like puzzles with a 'logical' solution far more than nonsesical trial-and-error puzzles. I saw one puzzle- a room with a cluster of pillars in the middle and floor switches around the sides. Each pillar in the room would disintegrate if you stepped on a specific set of switches. If you destroyed enough pillars, it would reveal a chest in the room's middle. There was no way to tell which two switches had to be stepped on to destroy a specific pillar; you just had to walk around randomly mashing switches till something happened. It takes from 15 to 45 minutes-what an obnoxious puzzle! I think the original Myst game did it right. Complex puzzles, but with logical solutions - if you were careful enough to observe the clues- assemble the cogs in a specific order and that lets you turn gear to open a large door.
How much Content:
Long/big is nice, but mainly it has to be consistently entertaining. I would much rather see a short quality game than a huge repetitive/meaningless game.
