Parenting an IK handle to the joint hierarchy it controls is not going to work. IK handles control the joints, not the other way around. So parenting a IK to one of the joints it controls (or a joint further from the root) will always cause problems, since the IK wants to tell the joint where to be and the joint wants to tell the IK (circular dependency)
Instead, you can:
Parent it to some other joint heirarchy that's used for control (common for reverse foot)
Parent it to a control box. You can then hide the IK handle and just move the control box around
Create a group with the handle and the joints as members.
Instead of parenting, you can use constraints to connect it to some control structure as well. I often do this so I can group controls separately from the actual rig.
Some combination of the above.
Other things I probably haven't thought of.
Typically, parenting it to a control structure of some sort is best. The idea here is that the control structure can be of a size and location that is convenient for manipulation, rather than trying to grab the handle, which is often hidden by geometry.
Hope this helps!