When it comes to polishing silver jewelry or gold jewelry, I definitely think less is more. You don't want to devalue your precious heirlooms or investments by over-aggressively polishing your jewelry. Now, tarnish - on your sterling silver jewelry - is actually a product of oxidation. So when your jewelry is exposed to elements in the atmosphere like oxygen or even sulphur, it will tarnish your jewelry.
Evaluate the Silver Jewelry
I think the first thing to do is just to evaluate your piece, figure out what the best method for cleaning it is. Now, as I'm looking at this piece, I can see that the artist has hammered lots of little decorations - but in those decorations, the artist has actually applied a patina. So if I were to dip this in an ultrasonic cleaner, it would strip all of that patina that the artist gave the piece. Additionally, if I covered this with some sort of store-bought silver cleaner paste, it would remove all the patina and I think it would devalue this piece.
Wipe Away Silver Tarnish
So, I think the best thing for this is just to take a jewelry cloth and wipe the surface tarnish away. And you can see the tarnish has rubbed off onto the polishing cloth. You can already tell that the surface tarnish is removed, but the design patination is left intact. These polishing cloths are really easy to find. You can purchase them at a jewelry supply - any jewelry store should sell them. I really like this particular one, because not only does this polish sterling silver, it also polishes gold, brass, copper... Don't wash your polishing cloth, though. Once it's completely covered with the tarnish, then your polishing cloth is pretty much used up and you can get a new one.
Store the Polished Silver Jewelry
Once you're happy with your piece, the best way to keep it shiny is to take a simple ziplock bag, squeeze all the air out, and this should actually keep the elements away - it should keep the oxygen away, and it should keep your piece shiny and ready to use.