Cleaning solutions for jewelry with gemstones

What type of products and procedures do you recommend for the cleaning and maintenance of gemstones, i,e, Birthstones? Will one product clean both silver and gold? Does the "pearl" require a totally different cleaning? What is the best method for cleaning a diamond mounted on a gold setting?

Don't know what is safe on pearls, just that some cleaners aren't. For other jewelry/rings, a little liquid dishwashing detergent in water in an ultrasonic bath works well. Small ultrasonic jewelry cleaner ⇦ on eBay or Amazon [affil link] used to be sold as denture cleaners, but I haven't seen them lately. They seem to have been replaced by sonic cleaners which are essentially a buzzer attached to a small tank and are sold in some department store jewelry departments.

I worked for Zales for a brief time and you would be surprised what toothpaste and a toothbrush removes and also shines once rinsed and its safe on any jewelry application.