There are eight Precious metals* in total, but the IRS only allows four of them in tax-deferred and tax-exempt Retirement accounts.
Most investors choose from Gold, Silver, Platinum, and Palladium when they are seeking exposure to the Precious metals.
* Precious metals: Gold, Silver, Platinum, Palladium, Ruthenium, Osmium, Rhodium, and Iridium
From an Investment perspective the best Precious metal to invest in is the one with the greatest amount of overall demand.
Silver and Gold have been in demand as money for thousands of years. Silver has been used as a currency in every human civilization documented throughout history, without exception.
Central banks continue to hold Gold as part of their reserves even though the Gold monetary system ended long ago (1931 in Britain, 1933 in domestic US, 1971 internationally). In fact, central banks around the World have been on a Gold buying spree since the Financial Crisis in 2008. China and Russia have more than tripled their acknowledged Gold reserves since 2008 and several countries have doubled their holdings.
Neither Platinum nor Palladium have a historic role as money.
Gold, Silver, Platinum, and Palladium all have Investment demand.
Human beings have recognized Silver and Gold as valuable substances for literally thousands of years.
As investors, it is reasonable to assume that deeply-ingrained human nature isn't going to change. When push-comes-to-shove, human beings are going to, once again, rally around Silver and Gold as the foundation of a healthy economy.
Platinum and Palladium have only been discovered in the last 200 years so we can't say anything about human nature in regards to these metals. Because the IRS allows Platinum and Palladium in self-directed IRAs the metals will have some level of Investment demand, but that demand is likely to be trivial relative to Silver and Gold.
Platinum and Palladium are used primarily as catalysts (catalytic converters) in the automotive industry.
Gold is used in electronics, dentistry, medicine, aerospace, jewelry, and art.