In general, people buy physical precious metals just in case there is a (currency/financial) collapse, to have a readily available store of their wealth, and because they do not trust paper. If one wants to avoid the risks of owning paper (dollars, stocks, etc), buying more paper (gold certificates, ETFs, futures) doesn't make sense.
Lots of people are currently interested in buying precious metals. When regular Joes and Janes are racing to buy something, this usually indicates the top of that market (stocks, houses, tulips, etc). On the other hand, precious metals prices can continue rising for a long time yet, given the monetary policies of most governments. Whichever way prices go, the buying and selling of physical precious metals is right now a booming business.
As is usually the case with booming markets, there is fraud. Thieves have been known to sell old ladies bricks spray painted a golden color. Companies like Cash4Gold are allegedly buying people's jewelry for as low as 1/3 of the market price. Others are trying to sell various gold coins for much higher than the market price. And so on.
So, if you're interested in buying bullion, you have to be careful. It's easy to find a gold/silver dealer through a search engine, but how do you know what they're selling you is legit and not gold plated lead?
One good place to start is USmint.gov. They have a list of dealers of American Eagle gold and silver coins. These companies are not official dealers of US bullion coins, but their listing on the government website gives them some legitimacy. I would be more comfortable buying from them than from those that are not listed.
After you've narrowed down the list, be sure to check how long the remaining companies have been in business. The longer the better. Next, try to find out how long it takes for them to ship you your order after they receive payment. If the dealer goes out of business before your order is shipped, you may lose your money. Thus, try to make more purchases for lesser amounts, just in case.
Be sure to shop around. There is always a premium over the market price that dealers charge. Some charge more than others. Remember to factor in all transaction costs, including shipping and insurance.
One company that I've been satisfied with is the American Precious Metals Exchange, operating out of Oklahoma. They've always shipped a couple of days after my credit card payment was received. The package is insured and you have to sign for it. Note that they charge cancellation and other fees.
I've never bought from Kitco, so I don't know how good they are, but the website has a wealth of resources.
Northwest Territorial Mint is one to be wary of. Many people say they have great experiences with the company. Others disagree. They complain of long shipping times and unresponsive customer service. The company has recently settled a related lawsuit. The premiums they charge are at times significantly higher than other companies'.
One of the safest (and cheapest in terms of above market premium) ways to get your hands on silver is to buy "junk silver." This includes dimes, quarters, and half dollars minted in 1964 or earlier. They have around 0.715 troy ounces of silver per dollar face value (10 dimes, 4 quarters, or 2 half dollars). (So the next time you want to pay for something with change, check the years of your dimes and quarters. You might get lucky.) Given that coins are hard to duplicate (or maybe no one bothers because the face value is low), when buying junk silver you can easily tell if it's genuine. Many people are even comfortable buying it on Ebay.
If making large purchases, you might consider opening an account with a commodities broker, buying gold or silver contracts, and then requesting delivery.
Some pictures from Zimbabwe. Let's hope that's not what awaits us.
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