Gun cabinet, China cabinet, in my case Curio cabinet. It's all just a box. As far as size goes, I think that it will always come down to it's not enough. Finding that right size good luck. I think it would be best to say make it a size that you will never be able to fill because once you do you will just want another cabinet or closet. When you get into larger sizes that you create not only will you have to worry about being able to make it airtight or to seal but you will have to take into account that it will require a little more TLC with proper airflow or circulation rather and things of that nature which is the issue I am running into now.
My curio cabinet I will never be able to fill it is a couple of feet deep but about 3 ft wide at the base and 2 ft wide at the top and 6tf tall. The humidity holds steady but varies from bottom to top due to the nature of humidity. Either way I will say the joy of making one makes it even more special. As far as shortest depth from front to back, I would advise making it a convenient size to where you can pull out the shelfs on your own and not need a forklift to do such but not so narrow that it will only hold the length of one cigar lol. I went with tall vs deep and wide for that reason. That way I could do 4 shelves that hold a great deal and one shelf at the top that I keep my prime smokes in that is only 2 inches thick if that makes sense. It is all a matter of preference. Again, I would say make it large enough to where you will never fill it. That way you will not be having to build more down the road. If people are like me most cigar smokers like to have their boxes full. Once they fill them they either end up getting more boxes or buying more coolers etc.
Good luck with it.