Pluto is practically the worst place we could put a base. No resources, far from the sun (less energy available and more needed), no igneous activity, nowhere near Earth (meaning we need to e self-sufficient from the start and won't be able to invade Earth easily)...
Anyways, the moon ha great advantages. We can launch a sneak attack. Build some big railguns and prepare them; we can fire enough rounds to terrify them (and ideally cripple their military fleets), demand surrender, and ready a round of shots that would destroy their big cities or military bases in case they send someone up without our permission. We'd be able to see them before they could react, and there's no way they could react fast enough to a bunch of big rocks. If they acted, hundreds of millions could die.
Then we surprise everyone by using our world domination well. We'll do better than what at least half the world is used to, which is actually a pretty low bar to jump over.
Yeah, and we've kinda settled on mars. I mean think about it, imagine how expensive a attack on mars would be, yet imagine how it's possible if only enough crazy people wanted to do it!
I still don't get why. Any attack from Mars gives the groundhogs every advantage we would have attacking from Luna--time, seeing our ships before they could make it, etc.