Especially for the deer hunting part, normally would not use Full Metal Jacket or Match bullets for that - you want Soft Points - bullets that are made to have some amount of expansion. Targets and gongs may not know the difference in bullet structure, but performance on game needs appropriate bullet. So 140 grain soft point totally appropriate for hunting - likely not made any more, but 160 grain Soft Point Round Nose is awesome on game, within the 6.5x55 effective range.
For my own use - not formal target shooting, just plinking mostly - always thought would be "cool" to take a 6.5x55 on a moose hunt (like the Swedes do) - so I have a supply of Hornady 160 grain RN Interlock and also 130 grain Nosler Accubond for mostly anything else. I have a long barrel m1896, a CG63 and an m38, along with various "sporters" with varying length barrels - if bedding is correct, bore is clean, muzzle in good shape, they seem to be very good shooters.
If you are interested in learning more about them - the book "Crown Jewels - The Mauser in Sweden" by Dana Jones is a very good reference - good photos and drawings, does a good job of covering the progression from first rifles made in Germany for Sweden, right on up through at least mid-70's.