The older 6mm rem were originally marked as "244 Remington" on the barrel rather than "6mm Remington".
These older guns had a 1-12" twist rate and most(not all) would not stabilize anything much heavier than about 90grs in bullet weight with the types of bullets then available.
That is one of the major reasons the 243 winchester got out of the starting gates quicker than the 6mm Rem.
Winchester saw the 243 as a dual purpose varmit/hunting cartridge and Remington (in their marketing wisdom) saw the 6mm as primarily a varmit cartridge that would be used occasionally as a hunting round - So they twisted it at 1-12" to shoot lighter bullets the best.
Later Remington saw it's mistake and renamed the cartridge "6mm Remington", marked it's barrels as such and started twisting the barrels at 1-9" to compensate (or over compensate, given the 243 W only had a 1-10" from the start).
They twist some of them differently these days to allow for heavier/longer bullets (such as VLD target type and copper).
Your rifle from that time period (mid-70s) most likely has the 1-9" twist, but could be different(like a 1-10").
You can check it yourself to be sure if you'd like to:
1.Take a cleaning rod and install a cleaning patch that fits tight enough to turn the cleaning rod.
2.Insert rod w/patch in the end of your barrel (either end will work, but on a bolt action your can pull the bolt and insert from the receiver to protect the barrel crown)and push until you see the rod start to turn.
3.Take a marking pen and make a mark across the cleaning rod where it is at the edge of the barrel or receiver. Then make another reference mark on top of the cleaning rod near the handle.
4.Push the rod in slowly and carefully watch for the reference mark on top of the rod near the handle to make a full revolution and come back to where it was when you started (one full turn on the rod).
5.Make another mark across the rod where it contacts the barrel or receiver.You now have two cross marks on the rod that it took one full turn to get to.
6.Pull the rod back out, take a tape measure and measure the distance between the two cross marks on the cleaning rod. If it measures closest to 10" you have a 1-10" twist, etc.
To answer another part of you're question: The twist should be for the type of bullets you intend to shoot, but with factory barrels you are limited to what they sell you.
Most people go with at least a 1-9" to shoot the 105gr VLD type bullets for example.