The idea of space-born power generators that transmit their energy via microwaves has been around for a long time, certainly since the early 1970's, and it has a lot going for it although these were almost all intended to be orbital stations rather than Lunar based.
However microwaves are not very efficient at transmitting energy over long distances and the combination of the Earths magnetic field and atmosphere would pretty much negate the overall benefits of trying to supply our power needs from the Moon.
A rocket launching Moon base is a nice idea especially as water, in the form of ice, has been discovered on the Lunar surface and it would make an excellent propellant. The only problem I can see is that you would have to get sufficient hardware from the Earth to the Moon to build your Moon-base anyway but if you put all that effort into building a spacecraft in Earth orbit you could be well on your way to Mars and back at least twice over.
However I can see a good reason for building small automated mining facilities that would project lunar soil, that contained water/ice, into Lunar orbit to be collected for use in spacecraft generally.