For the grid movement, there should be an 8 way movement option, so that you could move your character diagonally, like in the original Mother (known unofficially as Earthbound Zero) game for NES, for example.
There should also be an option so that the character moves like a normal 4/8 way movement but has its movement restricted to the grid. I'm not quite sure how to explain this, but several old RPGs on the NES have this kind of movement.
Rather than moving 32 pixels each time (on a 32 by 32 grid) when the player presses a direction, the player moves as long as the button is pressed, just like a normal movement, but is always aligned along the grid.
For example, say if you move 2 pixels to the right, then pressed down. Rather than going down from your current position, the sprite would finish moving 30 pixels to the right then proceed to move down. Yeah, like I said I am really not good at explaining things but I hope that makes sense.
Also, I was thinking that it would be cool if there was an option to enable gravity (and I guess jumping as well) so that you could have a grid based platform movement like in Lode Runner (or Bananarama, an old klik game made by Natomic from a while back http://www.classic-trash.com/gameInfo.php?gameId=710).