I'm not sure what connectivity you have on your random Technics amp. But, the projector should be able to be connected directly to the XBox One and you should be able to see how good the image looks that way. This way you can confirm resolution and compatibility properly.
For audio, you should use the S/PDIF digital optical connection. There is no reason whatsoever to use HDMI if your old receiver doesn't support it. There is no sound advantage that HDMI offers you in this case.