How would you want a plot to be presented?

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Now I don't know much about storywriting, so I can only tell you what kind of storytelling I personally like in games:
I'm a big fan of ambiguity and stories that let the player fill in the gaps. I also like it when my motivation as a player stems from what I see and experience in the game rather than from something the game told me (be it in a flashback, cutscene or via a note/diary).
Take Journey for example: You're never told "You need to go to the mountain". The mountain is simply the main point of interest in an otherwise mostly empty desert so the player takes interest in it automatically and creates his own motivation to reach it. I find that a very elegant way of storytelling.

So in your example (and I have to remind you guys here, this is purely fictional fairy-land-dream stuff, I know that it would probably be way too hard to actually do this in a Custom Story), if the main character should exact revenge on someone, then I would like the game to make me want that, personally.

So instead of having flashbacks or telling me what the bad guy did to my character, I would like the game to make me hate that dude, right as a result of whats happening in the game. A simple (if somewhat stupid )example would be this:
At the beginning of the game I find a little NPC dog that follows me around. Maybe it would help me solve riddles, or warn me when enemies approach and it would just be an overall loveable character. I feel safer in the dark with that adorable doggie around and the game makes sure I develop emotions for it. And then that asshole kills it. Right in front of my very eyes.
Now like I said, it's a pretty stupid example, but still, that would give me at least ten times as much motivation to beat the crap out of that bad guy than a thousand flashbacks in which I see him kill my family and burn my house down and whatnot. Because he has hurt me, the player, not just the character I'm playing.