I don’t really like when the story starts with a later plot point or ‘cliffhanger’. I think it’s just so cliché (but of course it can be done good). I also don’t like very much narrations, when we see black screen or the MC’s face with one animation for 10 minutes. It’s so boring, when the first half of the episode is just introducing, or we get the whole life story of the MC! I mean if something is plot-related, there’s many other ways to show it and if not, it’s just not necessary to add.
Oh well this went really negative. 
I think the best when you just start straight the story without narration/random thoughts about ‘the meaning of life’ or at least with only minimum narration.