I am very well versed in the kohler K series and magnums. My top favorite small engines of all times.
Some of them are really beat and knock / burn oil, but that is because they have survived long enough to be completely worn out.
Please keep in mind that no doubt, non detergent oils have been used in a 1970's engine, and as a result there will be a large accumulation of iron glitter and sludge in the bottom of the engine. Now that you own it, if you start using modern oils, you will essentially start to clean all that debris and begin holding it in suspension and create a lot of wear.
You will want to remove the oil pan and wash out the engine inside with a solvent. Then when you use a modern oil of your choice, do no exceed 25 hrs between intervals as these have no way to filter the oil. They shred lots of iron. They all will burn oil too. So keep it full.
I run 15w-40 / 5w-40 / SAE 30 diesel rated oils.. Do not run SAE 30 in winter.