The battery situation is your biggest concern here, and the hard truth is that those old lithium batteries are probably already degraded whether you use them or not. Leaving them powered off in a cool, dry place actually slows degradation more than anything else, so storing them in cases in a drawer is genuinely your best bet. Don't try to charge them regularly "to keep them alive" - that actually accelerates battery aging. If a battery's already dead, forcing charge cycles through it won't help and could potentially cause swelling or other issues.
For the physical storage, soft cases or even just some foam padding works fine to prevent rattling or accidental drops. Keep them out of direct sunlight and away from heat sources - a closet shelf beats a sunny windowsill every time. Don't store them in airtight plastic bags where moisture could accumulate; regular cases or just loose in a drawer with some padding is better. If you're really concerned about preserving them long-term, you could drain the batteries completely before storing (let them die naturally), then store them that way. Some people claim storing at partial charge (like 40%) is ideal, but honestly the difference between that and empty storage is minimal at this point.
One thing worth considering: if any of these still work and you actually want to use them eventually, you might get the batteries replaced now rather than later, since finding replacement batteries and technicians who'll do the work is only going to get harder. But if you're collecting them as-is, leaving them alone in cool storage is the right call. They'll outlast you sitting quietly in a drawer.