I would focus on items which will be impossible to manufacture post-apocalypse, because the industrial infrastructure will be gone. Interestingly, this does not include, for example, a hatchet or a knife; those can be manually manufactured from scrap iron which will be abundant. Also, if the chest is found the kitchen remains are found with it anyway. Knives will survive being nuked.
Which tools are most valuable? Some precision tools; probably a generator (to be connected to a windmill built post-apocalypse), possibly some copper wire.
Edit: These days, probably a sturdy foldable camping solar panel. No moving parts, minimal maintenance, life time of decades if you can live with performance degradation and nobody breaks or steals it.
A few select items which need power. Which ones? Not sure.