Numismatics is the study or collection of money, coins, and other related things. When you hear gold advocates talk about numismatics, they are probably talking about rare gold coins. You can buy coins that are worth more than their actual metal content. You pay more because of rarity and the condition of the coin.
There are rating systems for rare gold coins. For example, a gold coin could be rated MS 63, MS 64, etc. The higher the number is, the better condition the coin is in. These coins will actually come in a casing with the rating inside the casing. The MS stands for "mint state". The numbers range from 60 to 70, with 70 being a perfect coin.
I am not a big advocate of buying rare coins. It is purely speculative (although what isn't?). You are paying a premium for the rarity and condition of the coin.
I don't have any specific recommendations as far as owning physical gold vs. other gold investments. I think it is important to diversify, even here. Overall, I think it is a good idea to have at least a few ounces of the physical metal, but be sure to store it in a safe place.
If you are going to buy physical gold, I would recommend gold eagles, particularly if you live in the U.S. You can buy them in different denominations (one ounce, half ounce, quarter ounce, and one-tenth of an ounce). Aside from physical gold, you can own an ETF such as GLD, you can buy gold certificates, and you can buy gold stocks (although stocks do not necessarily track the price of the metal).
There is one really attractive aspect in speculating in rare coins. If we hit a gold bubble, you could easily see these coins rise to enormous levels and in multiples of the actual price. There is, of course, no guarantee, but I feel that I should point out the great possible rewards for buying rare coins.
There are also some major disadvantages. First, although all value is subjective, it seems to be even more the case with rare coins, if that is possible. It is the equivalent of buying art, in hopes that the next sucker to come along will pay even more than you did.
Another downside of rare coins is the price spread. I looked at one gold site and price spreads were in excess of $200 for something that costs just a little more than an ounce of gold. The price spread on the American eagles were only about $50. This is the difference between the buy price and the sell price.
If you are going to take a chance and speculate in numismatics, I would recommend you look at the American $20 St. Gaudens gold piece. The thing I like most about this investment is that you limit your losses. The actual gold content of this coin is just under an ounce of gold. Therefore, the value of the coin will never drop below the metal content. Right now, you should be able to buy one of these coins in MS63 or MS64 for just a few hundred dollars more than a one ounce gold eagle.
If you decide to take a chance and pick up a rare coin or two, don't forget to unload these first if we go into a bubble stage. You will not want to be holding these if there is a collapse in the gold price in the future. You can always just convert them to regular American eagles and profit the difference.