An Airport with USB drive is one possible.. or a TC which has a much faster internal disk is another.. however it is not designed as a proper NAS.
I recommend a proper NAS.. not cheap but hugely better performance.. and good selection from any number of brands.
Most will handle Mac and iOS just fine. But it is still not local storage.. and you should think out what is going to work and what is not..
Some Apple apps are not suited to network locations.. Apple specifically picks out iphoto.. although interesting photos uses icloud but not network storage.. which seems to be trying to force users on to the cloud.
External hard disk are better for desktop Macs.. faster, more reliable.. easier to backup.
You can also make it available to the network as storage.. and it will work as well if not better than a NAS. However NAS tend to offer larger disk sizes and more flexibility.