I've built several cases for individual ship models, but never a floor-standing one with shelves.
Some years back my wife and I decided that there ought to be a case full of models in the dining room. So we went to a furniture store and bought a curio cabinet. As I remember, it cost about a hundred bucks. (That was about twenty years ago; beware.) We've still got it; it works and looks fine.
Another good source, which several Forum members have used, is Ikea. I've had mixed experiences with that firm. Most of its furniture is designed down to a price; a sofa I bought for my stepdaughter cost less than a hundred dollars, but fell apart after a couple of years. And the fastenings of Ikea furniture tend to be a bit sloppy. But for the money it can't be beat. And it offers quite a few display cases: http://www.ikea.com/us/en/catalog/categories/departments/living_room/10384/ .
Building such a case should be well within the capacity of any competent carpenter. There are several sets of plans on the market, if you feel like you need one. Here's an example: http://www.leevalley.com/US/wood/page.aspx?p=45328&cat=1,46158,46161 .
I've never seen those plans, but I've done a lot of business with Lee Valley. It's a fine company.
One word of warning: wood - especially good looking hardwood - isn't cheap. If you make your case out of cherry (my favorite), walnut, mahogany, or oak, you're liable to find yourself spending more on lumber than a ready-made curio cabinet would cost.
Bottom line: good models need to be kept in cases. Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.