Best container for making sauerkraut
I use the German ceramic crocks. They come with stones that keep the kraut submerged and they have the lid that sits in a water filled moat. The company that made mine went out of business but there are other similar German/Polish fermenting crocks available.

The water seal does three things...it allows you to see bubbles coming out and lets you know fermentation is occurring. Secondly, it prevents organisms from the air getting in, and lastly, the oxygen gets forced out so all you have left inside is the CO2 given off by the anaerobic fermentation. You can use home brew airlocks to achieve the same effect. You would drill a hole in your plastic bucket lid, insert a rubber grommet and then add the airlock. Add some water to the airlock and then watch for the bubbles to start.

The only problem with the moat is the water can evaporate out and you lose the seal. Oxygen gets in and your anaerobic environment is lost. There are jars that only use an airlock, no water seal, so in that sense, the jars with the airlocks are better.

The side handles on ceramic crocks are sometimes not very functional. They can be hard to get a solid hold on, especially if your hands are wet.

I know lots of people use the open crock method. I have only used the closed crock. I believe anaerobic is best for getting the best bacteria but I am sure there are people who will argue open crock is better.

In the end, what's "best" is subjective. Functionally, I don't see why the food grade plastic bucket or the garbage can wouldn't work. Why it went bad...maybe the kraut wasn't covered or your brine concentration was too low. Use canning salt for your brine. It has no iodine and no anti-caking agents. It takes a while for the lactic acid to build up. That gives the kraut its flavor but also provides protection from unwanted microorganisms. Avoid the temptation to look inside (if using a closed crock) for the first 10 days. Let your kraut ferment at least a month. You could start eating it at 10 days but it needs more time to really complete the ferment. 

Funny thing is...I don't even like kraut. I have some home made in the fridge right now. It's been in there a year and I am sure it's still perfectly fine to eat.