You should NOT store your jewelry anywhere humid, such as the bathroom. Moisture will increase the discoloration speed with which the silver tarnishes.
*An anti-tarnish jewelry box or pouch.
*A small jewelry zip-lock bag. These make a perfectly good solution to storing your jewelry, as they are airtight. However, you should store your pieces in their own individual bags, to prevent scratching.
*A regular jewelry box with an anti-tarnish strip or silica gel packet placed inside it.
If you follow these basic guidelines, then your jewelry should last for long time, shiny and scratch free.