A disk is quite varriable on hp needed, depeneding so very much on soil type, angle of the blades, and spacing & size of the blades.
In good conditions in light soil to chop up trash you can handle a 20' disk well.
Some of the big offset disks meant do do deep tillage will make it work hard at 12'.
You likely will do fine with a 12' or so regular old wheel disk. Some 18-20' models fold up the wings, so you can use it as a light disk at full width, or fold up & use the extra weight to rip into the ground deeper as a 10-12' disk.
Most allow you to adjust the angle of the blades. Most have worn blades, and small blades do not cut well. It pays to spend more for a disk with good blades. Should be close to 20" across. Walk away from anything at 16" or less - this will not cut up sod.
Also bearings like to wear out, check those closely. A long job to take a whole shaft apart to replace an inner bearing....
--->Paul