If you want to deliver a smile with the highest social value, make sure it's genuine. According to Bangor University research, people prefer smiles that are genuine much more than those that are merely polite.
In one study, pairs of strangers were introduced to each other. Researchers observed that participants always reciprocated the smile type of the other person, whether it was genuine or polite. However, participants reacted much more quickly to genuine smiles than polite ones, perhaps because they were anticipating them as a form of social reward.
Here's the difference. According to a ScienceDaily article, "Polite smiles, for example, typically occur when sociocultural norms dictate that smiling is appropriate. Genuine smiles, on the other hand, signify pleasure, occur spontaneously, and are indicated by engagement of specific muscles around the eye."
The best type of smile is known as the Duchenne smile, which stands out because it extends the mouth further and makes crow's feet at the outer corner of the eyes.