I have two cases, a hard one (came an Ariette I had bought), and a soft one I had bought from Larry Miller for about $35. It can be carried like a back pack or briefcase, and is very light/small.
So, the best type of case will be a function of what/where you go when you take your box out of your house.
After using my softcase, I haven't used my hard case at all. When I fly, I take it with me. Someone told me that Wal-Mart had some hard cases made for some video games that fit a box well (HA-114) for about $20.... you can check that out too.
Personally, I vote for soft case.
What I used for a while with my accordion was an insulated soft sided 12-pack beer cooler that I lined with fabric. Just the right size and worked great... a little temperature protection too. Larry Miller makes a pretty nice wooden case covered with that grey furry stuff they use on speaker cabinets.