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.

1. 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.
2. 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.
3. 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.
4. 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. 
5. 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.

Suppose an 8-year-old, a 30-year-old, and a 60-year-old walk into your club, all beginners, and sign up for lessons. Suppose you were their coach. You'd likely start them off similarly, teaching the fundamentals. But something happens after a time - how you teach them begins to change quite a bit. You, the reader, should decide where in this spectrum your game fits, and perhaps discuss it with your coach (if you have one) or take it into consideration when developing your game.

For the 8-year-old, you'd soon be teaching him "modern" table tennis - like, say, Ma Long. Once he has the fundamentals down pretty well, he'll likely be taught to stay pretty close to the table, loop from both sides, with feet mostly parallel to the table, even for forehands (except when forced off the table). He'll become a great counter-looper. He'll mostly serve seemingly simple short backspin/no-spin serves - third-ball attack serves - and follow them with loops. (He'll learn other variations, but they will be "surprise" serves, not his core serves that set up his third-ball attack.) He'll learn to attack short serves with backhand banana flips. And he'll be well on his way toward being an elite player, maybe a contender for the National Team or more!!!

Many coaches would teach the 30-year-old the same way, but that's probably a mistake. If he's a truly top-notch athlete, then perhaps you would teach him the same way. But in essentially every case, he's not ever going to be in contention to be a National Team Member. His goals are probably to be as good as he can be - perhaps someday a 2000-level player. For this player, you would likely teach him a bit different - more "old-school." He'll learn to loop the backhand against backspin, but in rallies, he might be better off hitting and blocking aggressively. He probably should move the right foot (for righties) back some for forehands, and not try to jam the table when looping. He'll learn to counter-loop, but he'll pick and choose when to do so rather than trying to do it almost every time. He should learn to flip serves but should probably focus more on pushing them back effectively. And while he should develop short backspin/no-spin serves, he'll develop a wider variety of serves, especially deep ones - serves that don't work as well at the higher levels but can be dominant against players under 2000 and often higher. 

Of course, you should check with the 30-year-old to see what his goals are. He may want to play like Ma Long, in which case you'd coach him the same as that 8-year-old. (You should warn him that he'll need to put in a lot of hours to make up for lost time and have to be in pretty good shape physically.) How about a 20-year-old? He's in between, and depending on his goals and fitness level, you might teach him like that 8-year-old.

How about the 60-year-old? Unless he's a super-athlete for his age, he's not going to learn to run around all over the place looping. To reach his potential, it might be better to develop a great blocking game, and perhaps a good smash. He might learn to forehand loop against backspin, but in rallies he should probably mostly hit the forehand. He'll develop the trickiest deep serves he can, though he should also learn to serve short. He might learn to backhand loop against backspin, but often he'll be better learning to push, block, and hit. In fact, if his goal is to be as good as he can be, then (and some won't like this), very often he should go to long pips on the backhand, even early on. That's the dominant style at the older age groups, and there's a reason for it - the long pips is basically an "equalizer," allowing them to better block an opponent's athletic loops and turn all of that topspin into change-of-pace backspin. Another option is short pips, which can help with blocking and hitting.

Of course, you should also check with the 60-year-old to see what his goals are. He may want to play like Ma Long - but unless he's in great shape, I wouldn't recommend that as he'd probably hurt himself! But he might want to play with "regular" rubber, rather than face the stigma some long-pips players get, or he might want to play more of a topspin game.

In the end, players have to decide what their goals are. I've considered using long pips on my backhand a few times, but I just prefer sticking with inverted, so I win or lose using roughly the same equipment as the large majority of my opponents - plus, as a coach, I'm a better practice partner this way, both in drills and games. But everyone has to make the best choice for themselves!

When you receive a serve, you really have three options.

1. You can return the serve passively, so that you rarely miss the serve, but give the opponent the attack. This often means either pushing long or a soft topspin return.
2. You can return the serve in a neutral fashion, where you take away the server's advantage and get into a neutral rally. This often means pushing short or a well-placed flip, often to the backhand.
3. You can return the serve aggressively, where you play riskier shots (and so make more mistakes) but get the initiative. This often means looping long serves and flipping short ones aggressively.

You should learn all three types of receives. All can be effective, depending on the opponent. You should probably also specialize in perhaps two of these, so the opponent has to react to both types of receives - while keeping the third as an occasional surprise. For example, against short serves, many top players focus on pushing short or flipping, while using the long push as a surprise. Others push long more frequently, but then catch the opponent off guard by pushing short. Others receive aggressively, flipping against short serves over and over - and then catch the opponent off guard with a short or long push. Find what works for you - but learn all three.

By learning all three, you not only have all three tools in your tactical toolbox for use against different styles, but it allows you to be unpredictable - and that is often the quickest way to disarm a server!

Next time you are at the table tennis club or at a tournament, watch some matches from the side, so you are looking directly along the net. Watch how low the serves cross the net. Do this at multiple tables for players of various levels. You may be surprised at what you see! Most top players will serve relatively low to the net - but there may be some variation there. At the lower levels, the serves cross the net consistently higher.

The importance of serving low is often way underestimated. Higher serves are, of course, easier to attack, but the more interesting contrast is between a sorta low serve (often attacked) and a very low, almost net-skimming serve (very hard to attack). But serves that aren't low to the net aren't just easier to attack; they are also easier to push aggressively.

Some top players have seemingly simple serves, often mostly serving backspin or no-spin serves. But what makes them effective is they are served very low to the net, so the receiver can't make an effective or consistent attack. And so the server knows he'll likely get a passive return to attack. Others may have trickier serves, but because they aren't net-skimmers, they are easier to attack - and the server can't rely on getting a ball to attack as often. Here is a Tip that might help, Serving Low.

Serving is considered the "trick" part of table tennis, and this is where you can be most artistic. While you don't want to rely too much on trick serves to win, having a few tricky ones really helps - both in scoring a few "free" points and making your other serves more effective since they have to guard against those "trick" ones. (If overused, receivers get used to these "trick" serves and often find them easier to attack then simpler serves, such as short, low ones that set up a third-ball attack.) "Tricky" serves are often long and spinny, but may also be fast and dead, which opponents often put in the net.

If you don't have a few tricky serves to throw at an opponent, and the opponent does, guess who is at a disadvantage?

However, most serves should be "third-ball" serves that are difficult for opponents to attack and set up your own game, usually some sort of attack. (Most should be short, and yet long enough so that the second bounce would be just inside the end-line. At lower levels, you can serve long much more.) But even third-ball serves can and should be tricky. Try varying the swing and especially the follow-through right after contact. If you are serving backspin, follow through with an exaggerated upward swing; if you are serving topspin or sidespin, follow through with an exaggerated downward swing. Use quick motions to make it tricky for the receiver to pick up the racket direction at contact. If you serve no-spin, use a big, exaggerated motion and maybe even grunt on contact.

Don't serve just to put the ball in play; the serve should put pressure on the opponent, set up your shots, and win you some free points!