Usually sleeves for competition (or any quilt show, really) have to finish at a minimum of 4". You never know what the hanging apparatus will be - a thin rod, thick rod, slat, chain. It varies.
The instructions up above for making the sleeve are spot on. I prefer to put mine on after the binding is on, but that's a personal preference.
The only other thing I'd add is to build in a 1/4" of give in the sleeve. Regardless of which method you chose, you don't want it to lie flat - you want a little bit of room in there to compensate for the rod.
I like these instructions (with pictures):
http://wwwbluemoonriver.blogspot.com...lt-sleeve.html
Does the contest require you use specific fabrics, and then are allowed to add in a few of your own choosing? Maybe they want swatches of that. Unless specified, I would image a 5" square would be sufficient.