From a purely theoretical point of view, the x39 case with a capacity of about 2.03 cc would be ideal for pushing bullets from about 50-60 grains at @3000+ fps or 70-80 grains at @2900 fps for varmints, and 90-100 grains at @ 2700 fps or 110-120 grains at @2500 fps for medium game. This makes it well-suited to the .243 and .257 range of bullets. The .264 and above bullets would range on the too-heavy side for this case capacity, and the section density would be on the low side with the lighter-end bullets (one of the inherent problems with the original 7.62mm diameter).
The .243 would give you a bullet range from 55 to 100 grains, while the .257 would give you a range from 75 to 120 grains. With a view to suitability for medium game, I would go with the .257 for the heavier bullet weights. Something to consider also is that the 6mm PPC, 6mm TCU, and the 6mm BR all have very similar case capacities to the x39, and therefore going that route would essentially be a reinvention of the wheel. The .257s, on the other hand, don't have an existing case size anywhere in the 2.03 cc neighborhood, so you would be breaking some new ground in that respect.
Hmmm, a "257 Rusky" or "25-39" cartridge...could actually SELL! I know I would be interested enough to try it. Been thinking about trying to load down the 250 Savage to make an ultralight recoil deer round for my daughters, but you might have a better answer.