-Do you have a preferred art style
Not specifically, just that it should tie into the game's overall atmosphere. Photorealism is cool and all, but the emphasis should be on making the game elements recognizable.
-How long should the game take to play?
The length of the game itself isn't as important as how long a game takes to play out entirely. If a game can be "beaten" in 10 hours, but has enough optional content to stay fresh for ten playthroughs, that's much better than a Final Fantasy style 100 hour slog, because it gets much harder to keep introducing new mechanics after hour 50 or so.
-What aspects of the game do you like to have control over
Pacing. Sometimes I want to sit down and lose myself in the game, and there are plenty of games out there that do that. But, other times I have to watch the dog, or get stuff done around the house, or otherwise multitask my gaming time. For the ideal implementation, check out the Civilization series.
-How important is challenge?
See Devil May Cry. The game should be more than capable of kicking my ass, but put in an easy mode so scrubs like me can still see the story play out.
-Whatever you feel is important.
If you're making a game with zombies in it, the shotgun needs to be good. And have enough ammo to not be a last resort.
Aside:
NOT JAPANESE THAT IS ALL THAT MATTERS. God damn it, I hate anime-esque games.
This condemnation actually demonstrates what's wrong with "anime style" visuals: anime is a medium, not a style. Far too many artists out there have seen good anime/manga, and tried to emulate the superficial details of the medium (big eyes, cel shading, etc.) rather than the stylistic elements WITHIN the medium that made what they saw good.