how to keep it clean

Giving away small jewelry cloths is a nice idea for the jewelry that has simply silver and beads, with no cord. The cloths are safe on pearls. Most liquid cleaners are not.

The "tin cup" style necklace is a bit harder to keep clean. You don't really want to run a jewelry cloth down it, because then you will get the cord dirty with the tarnish that you just wiped off your clasp or silver beads.

I used to sell liquid silver necklaces (those multistrand teensy silver "bugle" bead necklaces). They are not easy to clean, so it is best to avoid getting them tarnished in the first place.
We suggested that *as soon* as you take them off, you wrap them in plastic wrap (Saran wrap, etc.). - and be sure to squeeze all the air out.
That is probably a good recommendation for the tin cup necklaces as well.
We even stored our backstock liquid silver necklaces in the plastic wrap, to keep them untangled and clean.

It's a combination of the body oils, and then "static" exposure to oxygen (sitting in a drawer, etc.), that tarnishes silver. (For most people, their jewelry doesn't tarnish while they're wearing it. But once it sits there in a drawer for a couple weeks, especially after wearing it on a hot summer day... )

Another thought - you mentioned the jewelry box or a pouch. A pouch might work well for storage, because it would touch more sides of the jewelry. That might work better than the box, because with the box, most of the piece of jewelry is still exposed to the air.
But I haven't actually experimented with this concept at all.

I hope this helps!