The primary advantages to purchasing silver are the fact that it has over the decades slowly increased in price. It is thus safe and easily traded most anywhere. The second is that it can be purchased in small dollar values that fit any budget.
There are two types of silver easily available: bullion and coins. Bullion is the term for privately produced silver rounds (they look like coins but can't be called them for legal purposes) and bars. Coins are produced by governments and include both fancy, large ones produced by modern mints and the smaller dimes, quarters, 1/2 and 1 dollars minted before 1965, when the US coinage still operated on a precious metal basis. These are some of the easiest since they are universally recognized and have a set, easily compared weight (so a quarter has 2.5 times as much silver as a dime and a dollar has 4 times the silver of the quarter).
So, how to know what a fair price is? Start off by checking the "spot price" for silver, either in your newspaper or on a site like CNN Money. This will give you the price of a Troy Ounce, or $1.40 face value of pre-1965 coinage. I have constructed a spreadsheet on OpenOffice Calc (you can use the same formulas in Microsoft Excel) where I can put in the bullion price (cell C4) and it automatically tells me the spot prices for various other values as well as what they would cost with markups of 10%, 20%, 30% and 50%. Smart sellers always have a markup, so don't expect to get spot price most of the time.
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If you have any questions don't hesitate to ask!