There are a wide variety of sets of United States coins that are worth collecting. If you have not yet decided to concentrate on one particular set, consider starting a collection of the various coin types - a series of coins of all different designs. If you do decide to do this, rather than just obtaining just any date or mint of a type, consider collecting certain dates that seem to have a greater potential for an increase in value. Naturally, these are just my opinions, but they are representative of dates and mints that are scarcer than usual and will certainly present your collection in a different light.
The first thing to realize is that the consideration of the total number of pieces produced (or minted) is not always the answer to pricing. The popularity of a particular set is a strong consideration, along with the alertness of the general population to the scarcity of a particular coin at the time that it was released into circulation. A classic example of this is the 1931-S Lincoln cent. With a total mintage of only 866,000 pieces, it was recognized as a low mintage date immediately and was saved in very large numbers. Hence the value in good of only $42 and a very low cost of $82 in un-circulated. Compare this to the 1914-D with a cost of $110 in good and un-circulated at $1,150, although the mintage was 37% higher at 1,193,000. The 1914 was not a low mintage at the time, and the Lincoln cent was new, with few collectors of the day. So, low mintage does not always equal high value, but it may be a guide to total availability.
Since there are many expensive coins in the following series, I will usually recommend that you purchase the pieces as slabbed - encased in plastic - with their grade and genuineness guaranteed by an independent grading service. This is especially true for certain coins, since they are often counterfeited. Purchase of non-certified coins are usually at your own risk, unless you know the coin dealer very well and he or she will refund your money if you later learn that the piece is not genuine.
In addition, many of these coins will not be available at every coin dealer, nor at every coin show that you attend. As with anything worth doing, it will take time and patience to acquire the pieces that I am going to mention, but, in the end, you will have a very worthwhile collection, and a very unusual one.
Starting with the smallest denomination coin that the United States ever produced, the half-cent is an obsolete coin. Obsolete because it is no longer used, although it is still legal currency of the United States. There are five major types of half-cent designs, so I will only look at one, the Braided hair design, minted from 1840 to 1857, the last year of production of the half cent.
Ignoring the proof only dates, we have mintages that range from 35,000 pieces to a high of 147,000 pieces. Considering that the coins vary very little in price, why buy a date with a mintage of over four times as much when you can have a scarcer date for nearly the same price. Any date in the series is a good bet, with the 1849 and the 1850, with production of about 39,000 total, as possible good dates. In good condition they will only cost $32 to $38, and in high grade, extremely fine, they are only $90 and $100 each. Not bad for a coin that has a nominal production and is over 150-years-old.
In large cents there are also a number of specific types of designs, so, since space is limited, I’ll only look at one, the Coronet obverse minted from 1816 to 1857. A common date is about $9 in good, with mintages of up to nearly 10 million, while the 1857, with a small production of only 333,000 will cost $45 in good. Again, this coin is 30 times the original production, or a scarce date, for only five times the cost. Note, I did not include the 1856 in my comments since many collectors do not include it as a part of the set because it was originally a pattern coin, and with a mintage of only 2,500 pieces (estimated) it will cost $5,600 in good condition, certainly not a reasonable price for a coin, although one that I would love to own.
Before the popular Indian Head cent series, the first small cents produced were the Flying Eagle cents, a beautiful design that was only produced for two years. Both years of regular production saw large mintages, so either year would be a good addition to a set. There is one variety, the 1858 over 1857 that is very scarce and popular. The variety occurred when a prior year die’s date was re-dated with the next year’s date. This was a common practice at the early mint, since the steel for the dies was very expensive and the mint tried not to waste anything.
There are many years with over-dates throughout the history of the mint and they would make a wonderful collection by themselves. Since a regular date is about $27 in fine condition and the over date lists at $175 in the same grade, I would definitely consider the variety over a regular date.
In the Indian head cent series, my favorite date is not a key piece, it is the 1908-S, a semi-key date. Minted in San Francisco, it is the first minor coin to have a mintmark and there were only 1,115,000 made for circulation. While the 1877 and the 1909-S are far more valuable, this piece has history written all over it.
The great San Francisco earthquake had taken place only two years before, and the people were just getting their lives back together. The last thing they cared about was collecting coins. Perhaps that is why it is priced a bit higher than expected at $61 in good condition. The date is available and it should not be difficult to locate a nice example.
As mentioned above, in the Lincoln Wheat reverse series, from 1909 to 1958, a popular low mintage date is the 1931-S. With a total production under one million, and many saved in high grades, we have a combination of low mintage with a very reasonable price. My vote for the Lincoln is the 1931 S in good at $42 and un-circulated at $82. It is a great coin at a very reasonable price.
Then there is the two-cent piece. Minted from 1864 to 1873, there are many common dates that will probably increase in value, but why not consider adding the 1872 to your collection? With a mintage of only 65,000, it is certainly a scarce date. Consider that an 1864, with a total mintage of nearly 20 million, sells for $13 in good condition, and the 1872 is $160 in the same grade. Sure, that is a considerable amount of money, but the 1864 has over 300 times the number of pieces that were originally produced.
The 1872 is only a little more than 12 times the price of the common date, yet is considerably scarcer. In the last five years I have seen, literally, thousands of two cent pieces at coin shows, but only one 1872. I now own it and it has increased in value since I purchased it to nearly double my cost.
Now is as good as any time to start your collection. Collecting coins does not always guarantee a profit, but knowledge and some research will generally increase your odds for success.