Good! It's the inputs that are most important. Simple adapters will work on balanced inputs. It the balanced-differential input that ignores common-mode and ground noise. You don't need any kind of fancy "converter". (Creating balanced outputs is more tricky.)
I'd try RCA-to-RCA first and if you have hum problems get some adapters for the amp inputs.
No, you want the converter at the RCA output, and a differential cable in between. Then any hum and noise pickup is developed on both high and low conductors equally, which is cancelled out at the differential input. If you run a single ended cable, then convert at the amp input, you achieve no rejection of hum and noise, it all ends up on the high input.
See the diagrams that
@sam_adams showed in post #5. The STP cable does the SE to diff connection at the RCA side. Likewise you can put the RCA to XLR adaptor on the RCA output, then run a XLR cable to the amp, which gives the same circuit as the STP cable.