It is personal on which rules you use. I prefer to only use the right hand palm rule.
The thumb of your right hand always represents the current. (One current, One thumb)
The fingers of hand represent the magnetic field lines (Many lines, many fingers)
The direction of the palm is the direction of the force (Your palm is used to clip your brother or sister over the ear which is a force)
So for any problem you will point your thumb in the direction of the current, fingers in the direction of the magnetic field and palm in the direction of the force. When you orientate two then the third only has one direction possible.
If you are looking at induced currents then the only thing to remember is the force will go in the opposite direction to the movement as it is trying to slow it down.
If you are looking at a positive charge then you point your thumb in the direction of movement of the positive charge as they move in the direction of current.
If you are looking at a negative charge then point your thumb in the opposite direction to the movement as negative is the opposite to positive. (Some people prefer to use the left hand for negative but everything else remains the same)