LEDs are the most stable/long lasting technology vs. VFDs (losing vacuum), LCDs (temperature damage), etc., you just want to under-drive the specification to get maximum lifetime. Beyond that? Not sure there's that much you can control for without extensive testing.
My method would be pick your type (7 segment, alphanumeric, dot matrix), pick a decent vendor, pick a part with a good lifetime specification, then drive it at no more than half rated current (less if it's a hot environment). Even mediocre quality LEDs could probably get well over 100,000 hours or more of lifetime under those circumstances, and since they're light, small, and solid state, they're not going to run into many of the physical issues that can come up with long term storage.
LCDs probably last fine but the size of the screen and relatively less support in the center can be more prone to damage, and unless you get screens rated for a wide temperature range, even freezing temperatures can do permanent damage, so they're probably not ideal for anything you expect to last through uncontrolled climate storage, though the technology itself is very long lasting.