Sterling Silver is a commodity like gold, albeit not on the same scale, and will rise and fall in value. That said, even if you have old broken jewelry that is tarnished and unwearable you should collect it and store it in a baggie. When it gets heavier, take it to a local jeweler who will weigh it out by the gram and give you cash or credit towards a purchase. Make sure your bag contains solid Sterling marked .925 and no plated items.
Sterling Silver will tarnish (oxidize) the more it's exposed to air. It's a softer metal and will scratch easier so store your Sterling in a sealed baggy. Anti tarnish baggies are best or a baggie with a small anti-tarnish slip of paper. Treated polishing cloths will remove light tarnish and keep your jewelry shiny. Brands differ and some remove fingerprints and less tarnish so Backstage Attitudes sells polishing cloths that are used in the finest jewelry stores and we often put a sample in with jewelry purchases.
Soapy jewelry cleaners wash jewelry but aren't very good at removing tarnish. Never use cleaners with a strong Sulfur smell like Tarnex as it will also take the polish off and leave it dull. That said, if you already did that you can take your jewelry to a local Jeweler who will buff and polish it on a machine with a jewelers rouge compound to make it shine again.
The best cleaner we've found is Wright's Silver Cleaner. There's a liquid to wipe on and off and a cream to rinse off. We find the cream in the jar faster to use. It makes Silver look brand new and you'll want to clean all of your Silver with it, not just your jewelry. Wipe on, wipe off, pat it with a soft cloth and let it air dry completely on a towel. Be sure to put it back in a baggie to keep air from tarnishing it again!!
You can find Wrights Silver Cleaner at Home depot and Walmart for under $6 or go to Wrights Cleaners. Home Depot had the best price last time we checked.
Wrights Siver Cream