Well, for me, I look for what flows well when read out loud.
Sentence structures that make for well-timed pauses, a lack of grammatical errors, and a bit of exposition around dialogue (unless it's a monologue, reminiscent to Damnation 101) are good examples for me, the latter being because back-and-forth dialogue without any tags can be difficult to read aloud with only one voice. In first person, characters with an interesting tone or voice are usually fun to read as well.
Another thing that I usually jump to, admittedly, is the ending. I'm a sucker for a good, dramatic ending. :) Cliff-hanger endings or endings with an unfinished conversation usually turn me away somewhat, because--again--that kind of thing can be difficult to convey in an audio format.
Keep in mind too that these are just things that make an ideal piece, and don't necessarily make or break whether I "decide" to read something or not. If other narrators would like to contribute to this as well, I'm sure you'd get a few different perspectives! I have no gauge on how picky (or not) others are. XD
I hope this answers your question a bit! Lmk if anything needs clarifying.
I'm not to picky, I'll pretty much read anything and every thing.
I don't like very__________ long stories, but ill do it if need be. I personally don't want the author to write a story just to fit our needs, It needs to be what ever comes to your mind.
If i do narrate a along story though, it does take a extra few days to produce quality video, compared to the shorter ones which can be done in one day.
And I also agree with the sentiment of not writing a story just to match any narrator's needs. :) Though it may be nice to take some things into consideration, if that's what you're aiming for, I find that the best stories are not forced and are written how you want them done.
Seeing all the recent stories the "big" narrators narrate, things like "I'm an edgy little angst shit who can't write and bought my dad on ebay", they seem to only be looking for stories, preferably ones just under 10min.
Like, the quality has dropped big time, I think most narrators have seen this as they started branching out into horror games and top 10's.