Principals of storage
Once the cabbage is prepared and stored in the container, the vegetables need to be kept submerged in the brine to protect them, and outside air kept out if at all possible. As the cabbage ferments, and the lactic bacteria get to work, they create anaerobic conditions in the brine and produce CO2 gas which also creates an anaerobic 'atmosphere' inside the container. These bacteria then ferment the vegetables. This also causes pressure to build up inside the container.
Which container to use
Traditionally people in countries like Germany used fermenting crocks, like the Harsch Fermenting Crocks, which have specially designed weights to keep the cabbage submerged in brine, and with a groove receptor for the lid, which can be filled with water which allows the CO2 to release, but does not allow air in. These are very clever but are also very expensive.
I have found that the best affordable containers to use are the canning jars which have a clamp like the one pictured on the right. These are designed to withstand a pressure inequality with lower pressure in the jar than out side it (as usually these are filled with hot goods and left to cool creating the vacuum effect), which means that as the pressure builds up inside the jar the lid will lift just enough to let out the pressure, but will not let outside air in, or at least not enough to have an effect on the atmosphere inside, imitating the effect of the traditional fermenting crocks. Kilner/Mason jars can also be used, but these do not release the pressure in the same way and it can damage the lid (although replacement lids are fairly cheap).
Most importantly, be sure to purchase jars which have an airtight seal. There are cheaper imitations which look the part but do not provide a good seal and let too much outside air in resulting in poorer taste and sometimes in moulds appearing on the surface of the sauerkraut.
Materials to avoid
You should avoid plastics, as even food grade plastics can leach some chemicals, and avoid metal containers, as the salt and fermentation can corrode metal surfaces. Best materials are glass and ceramic.