When I do mine I ferment it right in the jar(s).  I put it in wide mouth jars then use a 1C. Jelly jar with narrow mouth filled with brine to weight it down. 

That being said, depending on how much you're making – if you're making a lot - using your stainless steel, a gallon jar, or even the insert from an old crock pot works well so you don't have to work with a bunch of jars!  Main thing is that the container you're making it in is not a material that will corrode and leach into your ferment - which is most metals but especially aluminum.

The sauerkraut needs to be kept COMPLETELY under the brine so you need some kind of "pusher" (in your case the pasta insert) then a weight on top of that to be sure the sauerkraut stays totally under the brine.  Since it's going to expand and create some "gas" during the fermenting process, just be sure you have some head-room in there for that process (and thus, the scum).

A good idea for your weight is a plastic bag(s) filled with brine.  The weight of the brine bag(s) sitting on top of your pasta insert helps keep your fermenting product under it's brine and it doesn't matter if the bag breaks or leaks a little when you're tending things as it is fine for the brine to get in your ferment! 

As far as knowing when it'd done – it's a matter of how you like your sauerkraut to taste.  After about a week, just take a small taste every couple days.  Some people like theirs very "sour" and others like it a little milder – all a matter of taste!  And…it will ferment faster if your room temperature is higher – slower if your room temp is colder – so that's another reason the recipes state such a wide range of time!

When it tastes like you like it, you can then place it into the fridge or a cool area like a root cellar and it will keep for several months.  (Or you can heat-can it.)  The advantage of leaving it as a fresh ferment is a lot of very healthy nutrients that are created in the fermentation process are destroyed by the heat.

One thing you need to know – sauerkraut is STINKY when it is in the ferment process.  Cabbage is a strong-smelling vegetable in the first place.  If you've never smelled the fermenting process, I didn't want you to be surprised!  It puts off some pretty strong-smelling gasses so…be forewarned!

So far I haven't experienced a lot of the "scum" in mine so I haven't needed to skim!  Who knows what the future holds, however….

Like Buckeye Girl was saying, if you have any of the cabbage or other ingredients floating to the top, you need to remove it.  When it comes in contact with the air, it provides a place for yeasts (aka molds) to grow.  Fermenting is an "anaerobic process" where your product needs to be completely under the brine while fermenting to prevent the molds from getting in there.

Here are two links that may be helpful.  The first is from the Purdue University Extension regarding fermenting sauerkraut.  In the end they state that you can keep it in a cool/cold place, freeze it, or can it:

http://www.ces.purdue.edu/extm…..-610-W.pdf

The second is from the "Wild Fermentation" website.

http://www.wildfermentation.co…..sauerkraut

My parents used to make kraut everyother summer using a kraut cutter which my grandfather made. They put it in a 20 quart crock layering shredded cabbage with salt and placed a wooden circle a bit small in circumference than the crock to weight it down, then covered to top of the crock with muslin.  This was put in the basement to ferment and checked daily for unwanted bits of scum and cabbage.  I don't remember how long it was left to ferment but when it was "krauty" they packed it in pint containers and put it in the freezer.  Best stuff in the world with a bit of bacon "juice" and cooked with pork.  Yummmmm.