The voltage fed to the NES is rectified by an internal graetz bridge, and regulated down to 5VDC by a 7805 voltage regulator before being fed to the mobo. If the voltage is higher than 5V + the 7805's forward voltage when it reaches the 7805, the excess will be converted to heat in simple terms. With other words, the lower the feed voltage, the less heat dissipation. In my opinion, it's a good idea to keep the feed voltage as low as possible. The 7805's heatsink is somewhat underdimensioned...
You could of course calculate the minimum required feed voltage for AC or DC if you knew the forward voltages of the diodes in the graetz bridge and the 7805, but if I got a variable PSU, I'd simply experimentally determine the lowest voltage the NES would boot with, and use that, with a small margin upwards.
Theoretically, the amperage needs to be >= 1.3A, the same or higher as the original PSU's ditto. In reality, I doubt the NES consumption is even close to that. You could probably get away with using a far smaller PSU.
You can feed the NES either AC or DC. Polarity doesn't matter in the latter case, thanks to the graetz bridge.
To reply to your specific question, yes, a generic variable PSU at the 9V setting will work, as long as it can deliver 1.3A or more. It would however lead to unnecessary heat dissipation, use a lower voltage setting if possible.