Most would say there are three options - short to the forehand, middle, and backhand. (In this context, "middle" means the middle of the table. In other contexts, "middle" means the midpoint between the opponent's forehand and backhand, roughly the playing elbow.) But there really are five, and you should use them all, in varying degrees.
- Short to the middle. This is the most popular placement at the higher levels because it cuts off the wide angles. It also forces the receiver to choose between a forehand and backhand receive, which can both cause hesitation as well as draw the receiver out of position to play the forehand or backhand.
- Short to the wide forehand. Some players find the forehand receive against a short ball tricky, and this forces them to do that. Many players also have trouble returning this ball down the line, and so you can serve short to the forehand and know you'll get a crosscourt return. If the receiver has a good backhand flip (often a "banana flip"), then this serve mostly takes it away. If an opponent has trouble with this serve, then you can win a match off this alone. But it gives the receiver a big crosscourt angle, and the wide corner gives them a long diagonal to attack onto - so many players flip this aggressively crosscourt. If you have to cover that against an aggressive receive, you may leave yourself open against a down-the-line receive. Some players have trouble serving short to the forehand, as they have less table. If so, learn to do so.
- Short to the middle forehand. This is similar to serving short to the wide forehand, but it takes away some of the extreme crosscourt angle and the long diagonal. Also, since many receivers are set to receive against a serve short to the forehand, many find it awkward if the serve instead comes to the middle forehand, where they have may have to move to their left. Those who are used to flipping crosscourt may also find it awkward as their natural crosscourt flip will now go off the side of the table, and so may find it awkward having to aim more into the table. But it means it's easier for the receiver to get to this serve (compared to short to the wide forehand), and it allows them to receive with their backhand if they choose.
- Short to the wide backhand. This cuts off the wide angle to the forehand, so you can look to attack against crosscourt returns to your backhand. If you have a strong backhand attack, then this will often set it up. Surprisingly, this also is effective for forehand attackers. Since they don't have to worry about a wide-angle return to the forehand, they can edge over and look to attack with the forehand from the backhand side. However, the receive now has a wide angle into the backhand, and they have a long diagonal to attack into.
- Short to the middle backhand. This is similar to serving short to the wide backhand, but it takes away some of the extreme crosscourt angle and the long diagonal, while still not giving a wide angle into the forehand. However, unlike on the forehand, most receivers have little trouble adjusting between short to the wide and middle backhand, as the wrist is freer on the backhand than on the forehand. This serve is often done by righty players who serve out of the backhand corner (like most do) and makes it easier to keep the ball short while not giving the receiver such a wide angle into the backhand.