Sand works great for easy clean up as it semi-dries out the litter (poop) and makes it easy to scoop up. Your profile doesn't say where you are. Will mud be a problem during spring or rainy weather?
It is very hard to clean litter out of gravel and you will likely have an odor issue as it builds up.
The deep litter method is where you put down several inches of wood chips or straw over the floor. As the birds scratch around the material breaks down and the litter sinters to the bottom. You then add more on top to keep the birds dry and elevated above the litter. Depending on your area and material chosen, you muck out the whole works on a quarterly, bi-yearly or yearly basis and start fresh.
Here in Minnesota we use straw during the winter for warmth, but it gets moldy if wet. Wood chips are a better choice in warm or wet climates.