What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There are a few major varieties of the 1798 Draped Bust Large Cent (Penny). Two of them deal with the hair style on lady liberty on the obverse of the coin. "Style 1" features the older hair style with the absence of one curl of hair. "Style 2" is the newer type which features an additional curl of hair just above the shoulder. The difference between the Style 1 Hair vs Style 2 Hair is depicted above in the example comparison image of the coins.
Another variety features an older reverse using the Reverse of 1795. Sometimes this is known as "Reverse of 1796". This design features between 17-21 leaves on the left branch and 16-20 leaves on the right branch. The most distinctive feature is that there is only one single leaf on the top of the right-side branch - which is the Reverse of 1795 as depicted by the comparison image of the various reverse designs below. Typically the 1798 coins uses the Reverse of 1797 design and all draped bust large cents afterwards use the 1797 reverse:
The last major variety is the 1798/7 Overdate Error which features a 1798 date struck over a 1797 date which resulted in part of the underlying "7" still visible within and/or around the "8" as depicted by the arrows in the example image below (Source of example image is courtesy of Heritage Auction Galleries):