Anybody know the history of Vegas and basically why that location was chosen as the main hub for gambling, hotels, and entertainment given that (at that time) it was pretty much a random desert in the middle of nowhere?
Las Vegas was not founded in a particularly random desert. It was founded on a meadow (las vegas is Spanish for "the meadows") watered by the nearby Big Springs, or Las Vegas Springs. As such it was a watering spot on the Old Spanish Trail.
After the Civil War, O.D. Gass set up the first permanent white settlement there. Other settlers followed, and it was an important enough agricultural center to attract a stop on the San Pedro, Los Angeles & Salt Lake Railroad. This put them within a day's reach of Los Angeles and the sea, contributing to substantial growth.
As the nearest major settlement to the Hoover Dam, Las Vegas also enjoyed an influx of population and money during its construction, and cheap electricity and tourists headed for Lake Mead after its completion. They were boosted again with the construction of nearby Nellis Air Force Base.
The aquifer feeding the springs that had first attracted settlers to the area were sucked dry by the 1950s, but by then the city was already by far the largest population center in southern Nevada, and tourism and the military had long since displaced agriculture in the local economy.
The main reason that comes to mind at once are legal issues:
Nevada, legalizing casino gambling in 1931, was for almost 50 years the only state with legal casinos, New Jersey being the second one, in 1976.