Silver is invaluable to solder and brazing alloys, batteries, dentistry, glass coatings, LED chips, medicine, nuclear reactors, photography, photovoltaic (or solar) energy, RFID chips (for tracking parcels or shipments worldwide), semiconductors, touch screens, water purification, wood preservatives and many other industrial uses. Silver has been called and konwn for being "the indispensable metal".
If gold is the most well known precious metal, silver is easily second. Silver has more industrial uses than gold so it’s valuable as both currency and for its industrious properties.
If there was a ranking on “preciousness” platinum could be considered the most precious of all the precious metals. It’s 15 times rarer than gold and its more ductile than gold, silver or copper.
Related to platinum, both belonging to the elemental category called platinum-group metal or PGM. Palladium has some of the same uses as platinum especially with its use in catalytic converters.
Gold is the most well known precious metal for many reasons, but the most noteworthy is its strong ties to global economies throughout history. Used as currency in many countries globally for hundreds of years, makes it inherently valuable and can still be exchanged for fiat currency.