What do you mean by
Kp has a value of 0.534 at 960K and 1.571K.
Do you mean a value of 0.534 at 960K and a value of 1.571 at some other temperature?
which of the two equations should I use to calculate ΔGr°?
Well, which do you have the information for?
Note that this is not as simple as it may appear (though, as a homework question, they may be expecting you to use the over-simplified approach). Over this range of temperature (950 to 298K), ΔH and ΔS will not be constant. Also, the standard state of water at 298K is liquid, not gas.