Length of the average entry? They're kinda all over the place. Some are around 600 words - I've got one that's well over 2000. If you want to include characters and a story, it would definitely help me understand the premise for the game. After all, we're not asking for Dream Gameplay, we're asking for an actual game. Now, these characters and the story don't need to be totally fleshed out. Just give a good idea of what's going on. And like I said, the more detail you have, the better.
And I think you should definitely send in an entry. What've you got to lose?