I love lacto-fermented sauerkraut. It is so easy to make the real deal and it has so many health benefits. When I first started making it I used 1.5 litre jars. But now I have found a big ceramic pot that works really well. Not perfect - it has a lip that means I can't get a plate in to cover all the vegetables, but it does fine.
I basically follow the instructions here for making it. I chop my cabbage because it is easier than putting it through my decrepit and slightly broken food processor. Then I add lots of grated carrot and thinly sliced onion. Apple is also really nice. When you have your veggies prepared then you need to salt them. Add about 3 tbsp sea salt to 5 lbs veggies. I also like to add a bit of the last batch of sauerkraut to get things started but this isn't necessary. Mix thoroughly and then add to your container. You then need to give them a good bashing, to squash them down tight and to start to break down the cell walls of the veg. I use the end of a rolling pin in jars and my fist in the big pot. Keep pounding until you have all that tension worked out and the veg is tightly packed. Then you need to weigh it down with something. If you have a plate that fits your container then put that in with a jar full of water on top to keep it down. If not, then fill a plastic food bag with water, seal tightly and put on top. Over the next 24 hours keep pressing the veg down as you remember. Water will be drawn out of the veg by the salt slowly. After about 24 hours the veg should be covered. If it isn't then you can add a little more brine - mix a tsp salt in a cup of water and put in enough that the veg is covered. Then leave it to ferment for 1-4 weeks. After the first week then you can start to sample the sauerkraut to see if it is done to your taste. How long it takes really depends on the temperature and how much salt is in there. When it is finished you can store it in the fridge if you have space. If not then put it in a cool place and make sure that the brine is always covering the vegetables after you have taken some out.
Here are two rubbish photos trying to show my arrangement for fermenting sauerkraut. It is a ceramic bread crock from Tesco and a freezer bag full of water on top for a weight. If you are sitting down then have a look at the 'proper' fermenting crocks (click on 'wholesome gadgets' in the link). There - looks a lot less naff when you have seen the price of real ones doesn't it!