It amazes me, such a common problem that has been adressed so many times,in many forums.
Good batteries,clean connections and tight grounds leave the only thing left is a bad starter. Just one click then nothing else tells me it is battery or cable issue,will click with every turn of the key then voltage at starter needs to be checked, could be just a bad stud on solenoid as thats the solenoid contact. Not enough pull in voltage, like high resistance through neutral start switch.
First test is a jump at the starter itself.