On 20' boats I used 15' and on smaller boats 12'
12' is cheaper as that is the length aluminum is made, or 24' So if you want a 15' aluminum sprit, you need to buy 24' of alum, which is more expensive the carbon.
The farther out you go, the more the angle of the luff, and more the angle the more the lift up from the sail, keeping your bows from driving in.
With a very short sprit, you will probably be driving the hulls deep most of the time.
Also, the longer pole will open up the slot more.
Rick