It's great to hear someone still jumping with with the Cirkut. I've made my living with one for quite a long while. They are great fun, and I was thinking last night about how much I enjoyed figuring them out and getting them to work well.
The Cirkut shooters I know keep their negatives in the original Kodak boxes. Until the 50's or so (maybe later - all well before my time) the film came in a metal can inside the box. When I find old Cirkut negs they are almost always in the box or can. The cans seem to have provided some extra protection, but the problem with all these is obvious - the negatives set up into a strong curl over time. For 5-10 year storage I wouldn't worry about that. Long term it does lead to problems (some of my older negatives are hard to flatten for printing). I also realize you may be loading from bulk and not have boxes (a problem I had with b&w). I also don't know what kind of film you are shooting.
Shelves would be ideal. That's how I store my prints. But retrieving negatives would be a chore. Hanging sounds fine as long as you have space for it. They'll get dusty and be getting a lot more air transfer over the emulsion, but I doubt it will really be an issue for you.
I use 1.75" tubes for shipping prints, and sometimes use those for storeage. They are not acid free, but a sheet of acid free paper could isolate the negative from the tube if you are concerned. This last may really be the most practical solution.