What to collect is entirely up to the collector. It will normally be a specialization that holds some interest for the collector and is within his or her budget.
Among the most popular types of collections are world coins (coins from several countries), ancient coins, and coins of a particular country. Some specialization within these categories is ordinarily helpful. If collecting from a particular country, you can work on one or more series, a type set, commemoratives, errors, die varieties, paper money, etc.
You may also want to set bounds on the grades of coins you collect, e.g. all G-VG, VF or better, or un-circulated. You could collect an entire series. The goal of a series collector is to acquire one of each date and mintmark made, usually including any major design differences. For example, the U.S. Standing Liberty quarter was produced from 1916 to 1930 at the Philadelphia, Denver and San Francisco mints (coins were not made at all three mints every year, and none were produced at any mint in 1922); a major change to the obverse was made in 1917, and the full set is generally considered to include both designs for that year from each mint.
A collector building a type set seeks to have one of each series and major design variation within each series. Examples would be 20th century Canadian coinage or U.S. gold coins.
You may choose to focus on ancient coins. That is coins that were minted prior to 500 A.D. Many of these are in a theme and that is one way to focus your collection.
Experts say that the gold, bronze, and silver coins of the ancient world are actually quite readily available today and can be had for not a huge investment.
Tokens are also popular with collectors. When the government ignored the needs of the people and refused to issue sufficient low value coins the traders took matters into their own hands and issued tokens. In Great Britain this took place in the mid 1600's, the 1790's and the 1810's. These formed a local currency and it took several acts of Parliament to ban them. The bans were never completely successful and 'advertising tickets' continued to be issued through the mid 1800's. These were conveniently the same size as farthings, the coin still in very short supply, and undoubtedly circulated as such.
By the end of Queen Victoria's reign the need for tokens had gone but there were all sorts of other similar pieces being used. Pubs issued checks but because they were such an everyday occurrence nobody thought the record how they were used!
The co-operative societies used checks to record the value of purchases made so that the correct amount of dividend could be paid. Fruit pickers received tallies to depending on the quantity of fruit picked. The most recent use of tokens is probably the ones used in gaming and vending machines, as well as the one used by the many transport undertakings.
Although less valuable than coins, tokens are nevertheless much more interesting if you are interested in local history and like to do research.
You may want to look into collecting proof sets. Proof coins are specially manufactured for sale at a premium to collectors and sometimes for exhibition or for presentation as a gift or award. Proofs are generally distinguishable from ordinary coins by their mirror-like fields, frosty devices (especially in recent years) and extra sharp details.
To obtain these qualities, each proof coin die is polished to produce an extremely smooth surface and used for a limited number of coins. Planchets are hand fed to the coin press, where they are struck at a higher than ordinary pressure. Struck coins are removed by hand with gloves or tongs. Modern proof coins are usually packaged in clear plastic to protect them from handling, moisture, etc.