There are a few things at issue here:
Space - If space is at a minimum, typically I would look at wall mounting. In this case, you're looking at a cabinet with a glass or perspex front. A long wall may be required for pole arms, but typically you're looking at 3" deep hooks to support the item, which would mean you'd want a 4-5" deep frame. I would recommend either a book-hinged door, or a slide sliding front.
Cost - Museum Quality display cases are extremely expensive. For example, a small archival quality display case can be as much as $800 - 1000 USD. Much smaller vitrines will still cost at least half that. So why would you want to pay so much?
Museum Quality cases are usually made of treated fiberboard that does not off-gas, which means that your display is not contributing to the decay of the items you're seeking to protect from tampering to begin with.
Any suitably large display will require significant upkeep; low quality casings will require even more upkeep.
Value - Are these items of any monetary worth, or purely sentimental? Either way, a distinct budget should be created to determine what the value of their continued care is to the owner. This will determine whether the investment is immediate, or should be spent in greater sums over time.
Unfortunately, this is a generic question, so there's not a lot that can be said with any specificity.
Personally, for archival and display options, I would choose Gaylord Museum, or I would opt for a local company with experience building museum displays. I would make a list of all the items inherited, sorted by material (which would have different optimal storage humidity), and speak to a customer service agent to meet my specific needs.
A caveat, however; I'm the sort that believes that things worth owning are worth caring for. I own a few denshō which I keep in archive displays which cost more than the books did. These are my choices and may not reflect yours or your friends. This is why I believe "value" to be a key deciding factor; not simply price.