Biased poll, but at least you tried
It was clear to see which answers suit your preferences, though.
First things first, what I "actually want from Skyrim's story" is: TWISTS. Not in the sense of "oh no we thought the amulet was safe and now it's stolen", but in the sense of "this new character and his explanations turn this whole story upside-down! I'm
on the wrong side here and Esbern should be slain for his betrayal!"
That's one important question you've missed, in my opinion. Now, on to the other questions.
1) I want the story to start late. I like how they start with a bang, and have dragons appear everywhere, but I wouldn't like it if I had to jump into action right away. And I can think of several ways to slow down the progression of the story, so I hope they do that.
2) Personally, I never liked branching stories that much. I like the concept, but in practice it just doesn't work for me if it's somehow tied to moral or strategic choices that I have to make, because then I feel either rewarded or punished for that, depending on how it turns out; and I'm not a fan of that. I want to play my character the way I want without having to fear that I will trigger the bad ending or anything.
What I do like is choosing which path you will take to get to the same ending. For example,
Indiana Jones and the Fate of Atlantis had three completely different paths, with different locations and different story twists and everything. One was action-based, the second puzzle-based and the third teamwork-based, but mostly they were simply completely different in how the story developed - the labyrinth of Knossos serves a completely different purpose in each of the paths, to name an example. But once you wound up in Atlantis, it didn't matter anymore how you got there; the finale was a whole other story (and it was only in this last chapter that you could make choices that influence the ending). I would really like to see something like this in a game again, it was good stuff and each path was a lot of fun.
3) Grey shades should be extremely important in the game. I'm sick of good vs. evil, just like I'm sick of being able to make a choice whenever presented with a moral dilemma. Sometimes, things are just grey and there's nothing you can do about it. Complex moral circumstances make for interesting stories, especially if you sometimes have to do things you don't like.
4) I voted for "happy ever after", even though I'm not so sure about this. But I somehow have the feeling that many games now try to seem more "rugged" and interesting by giving you a bittersweet or bad ending. And often, that feels really cheap. A good happy ending is much, much harder to pull off. But sometimes, stories just manage to put a satisfied smile on your face when you finish them, and it's just so much better.