Hands down, the best way to ship your valuables including gold, silver and rare coins is to use the United States Postal Service's Registered Mail Services. While the post office employees may try to convince you to switch to insured mail, do not take the bait. In the terms and conditions, you will find the ugly surprise that this excludes lost precious metals UNLESS they are mailed with Registered Mail.
Registered mail is specifically designed for high valued goods such as gold and silver bullion. In fact, even the Hope Diamond was once sent via Registered Mail. The "chain of custody" is so safe that it is also used for "secret" documents by the United States government.
Registered Mail can be insured for up to $50,000, and you must declare the full value of the mailpiece when presenting it for mailing. USPS provides insurance which matches that declared value of the box, up to $50,000. This handling fee and insurance will vary depending upon weight, value and distance. For reference, a medium flat rate box insured for $1,000 and travelling across the country would cost approximately $35.00.
Registered Mail is so secure because of the "chain of custody." Instead of travelling with all the rest of the mail, Registered Mail packages are contained in locked containers. Each agent that handles a registered package signs for it individually, and is literally on the hook for it.
If a Registered Mail package goes missing, a serious investigation occurs (unlike when they lose your other packages). If a USPS agent is found at fault of losing it, they can be held directly responsible and are at risk of losing their job as well as their complete pension. This means that the post office employees have a mutual interest in making sure the registered packages make it to their destination safely.
Time: Registered Mail is slower than other services. Because of the additional security measures taken, don't plan on your package always arriving extremely quickly. The packaging is more difficult than your average box that you ship. The package must be tamper-proof, meaning that all seems must be covered in plain paper tape, or cloth tape. The tape must absorb ink and must visibly damage. This is often a tape that most households have, but is something you can easily buy ahead of time if you are planning to ship. (Note: USPS employees are not allowed to help you prepare or seal Registered Mail). For help packaging your Registered Mail package, check out the USPS site.
Additional Form: rather than just walking up to the counter, you must fill out PS Form 3806, Registered Mail Receipt. This is a really easy form to fill out, you just need to copy down the addresses off of your box.
You must also drop the package off personally, no pick ups available.