If you were growing them for commercial purposes and intend to pelletize them, you would need to get to 8 to 12% moisture content from an original 80%-ish. For your own purposes, it depends on how long you want to store them.
The first reason to dry them is to remove moisture that would otherwise oxidize/rot the cones and reduce shelf life. So if you intend to use them within 3 to 6 months, dry them down as best you can and freeze them.
Don't dry them down to the point where the stig breaks. At that point you are so dry, your lupulin is most likely falling out and you are left without the alpha acids you want for bittering. A 4 to 5 times reduction in weight is a pretty good rule of thumb.