First, there are many grading companies out there. In order for the graded coin to be accepted as being the grade it is claimed to be the person buying the coin must respect the grading company’s work. Most coin collectors will readily accept PCGS, NGC, ANACS, and IGC. PCGS is highly recognized, and NGC has a relationship with the American Numismatics Association.
ANACS was the first grading service in response to the need of collectors to authenticate coins as genuine, and is still highly respected as the authority on ancient coins. ICG is usually the grading services used for many Canadian coins.
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It depends on the value of the coin. I like capsules, since they protect against physical and environmental damage, but they cost one to three dollars, depending on the size. 2X2 mylar flips also do the job much cheaper, but mylar can tear and damage occur. It is also not as hard as capsules. Vyna flips are good for temporary solutions such as protection during shipping at a reasonable cost. The thing to remember is it is not a good idea to spend more than the value of a coin to protect it, which can easily happen even with Indian head pennies.
blackspanielgallery, What is the best way to protect coins when foregoing grading?