What should be the polarities of the op amp input terminals such that the system is stable?
At first, I assume using the term "stable" you intend to use such a circuit for linear amplifying purposes, correct? I further assume that the left nodes of R1 and R3 will be connected to common ground (as defined by the not shown double voltage supply) or to a voltage source.

Then, if the used opamp is universal-compensated (most opamps are) the circuit will operate in the linear region if the negative feedback overrides the positive feedback. For the resistor values as shown in your diagram this will be the case for the shown polarity of the opamps input terminals. The negative feedback factor is k(-)=0.5 and the positive feedback factor is k(+)=100/300=0.333.   

There are three different alternative operational modes: Non-inverting gain (R1 grounded), inverting gain (R3 grounded), differential gain (R1 and R3 connected to voltage sources).