Finding the Right Coffee Grind
In short, it's about extraction.  Too fast, and you don't get the right flavours and too slow and you'll get off and bitter tastes.

With a setup like the one you describe you can't change the speed the water passes through coffee (unlike espresso, for example) so you control how long water spends with your coffee (and the surface area of contact) by the size of the grind.  

The water will tend to stay and mud up super fine grinds.  If you were to try to filter through turkish grind, you'd be waiting a long time and might taste something harsh.

Too coarse of a grind and the water will run through and not pick up enough (low extraction).

Aside from colour, taste and aroma, what you are looking for is how long it takes for water to pass through the coffee grind.  I can't tell you how long for your specific setup, but if you're going slower than 20 seconds per ounce of water, it's likely too fine of a grind.  Also note that the longer water spends with coffee, the more caffeine it'll pick up.

Finally, if you can, keep an eye on the drips as they leave the filter.  When the drop or stream is no longer cloudy and starts looking clear, that's about when you've extracted what you can with that grind (both amount and coarseness).