I have been making it for years, even before the fermented food hype.
I don't sterilise the jar but certainly wash it very well with hot water and I empty the kettle in it.
I do wash the cabbage, because my best friend growing up had a farm and sometimes I would help out and see the seasonal workers, and nobody will lose 15 min of work to go to the toilet, people do their business in the field.
So, yes , wash your cabbage, even after removing the outer leaves.
To make sauerkraut, you need to make the cabbage cry. 1/2 cabbage will make a mason jar.
So after you cut it very thinly (I prefer to do it by hand), put the cabbage in the biggest salad bowl you have, add a teaspoon of salt, pull your sleeves up, and make the cabbage crack with your hands. Massage, squeeze, turn, for a good 15 to 20 min. By that time, whenever you lift the cabbage, liquid will just pour from your hands.
Put it into a mason jar, empty the liquid on top, push the cabbage under liquid and I usually use an egg holder as a weight that will keep the cabbage submerged once I push the lid against it.
Keep for two weeks on kitchen counter covered with a dark tea towel.
After two weeks, it is ready and needs to move to fridge.
No water, no liquid, not even spices, mustards seeds or herbs .