Technical question : 1080p @ 720p TV? Which machine should do the resampling?

[Deciazulado]

Which one does 1080->720 best, the TV or the player? You have to try both and see which gives the best results with movies and live action.

768? Yes, if the native resolution is 768 the display will have to do 720->768.
Some displays have a 1:1 pixel mapping setting. If yours has it you could watch 720 as 720. The image would be a little smaller (you'd see narrow black borders on all sides). But depending on the scalers quality and your seating distance, scaled 768 might look fine/equivalent to 720 straight.