This word's apocryphal acronymic association is absolutely absurd.
The story is that "POSH", an acronym for Port Out, Starboard Home, was printed on 1st Class tickets for travel between England and India issued by the Peninsular & Oriental Steam Navigation Company.
The original folk etymology suggested that the port side on the trip out would have the coolest cabins ... a curious theory since it assumes that the microclimate of a ship is capable of providing a significant temperature differential. It does not take into account the position of the sun, the direction of the wind, or the fact that as the ship sails South to Cape Horn the port side will face East on the other side of the cape, sailing North the port side faces West.
If the trip is through the Suez Canal, the time of year is more likely to be a temperature factor.
This being the case an alternate theory was concocted. This suggested that the port side would always be in view of the shore and therefore the scenery would be better. But ships, especially large passenger ships do not hug the coast. There are too many possibilities for disaster from weather or shallows.
Putting the death blow to this story is the fact that no tickets with POSH on them have ever been found, and the company records show no evidence of the phrase.
Merriam Webster puts the earliest publication of the acronym story in the London Times Literary Supplement of October 17, 1935.
But "posh," meaning a dandy, dates back to 1867. Some think it derives from a Romani word meaning half (used in monetary terms). Others, including Partridge, think it may be a contraction of polish.
To spin this etymological circus out yet further, I could make a case for some other derivations as well.
Posh -- from pasha a middle-eastern title for a ruler. Folklorically, pashas lived in great splendor and luxury. Luxurious items were sometimes described as "fit for a pasha." The phrase degraded and shortened to "pash" or "posh".
Posh -- a variant of pashe or paishe which itself is a shortened variant of "passion".
Posh -- a term used to indicate the luxurious decorations and vestments used in the church at "Pasch" or "Pasche" meaning Easter (Paschal season).