> Depending on where you established infrastructure on the moon, it might be pretty easy to conceal the things you're doing in space.
No it wouldn't be, because there is zero chance in hell of everyone else on Earth not realizing whats going on, if someone were suddenly busy launching all that machinery, building materials and weapons towards the Moon, not to mention hundreds of personnel with all their space suits, provisions, water, shelters, space poop collectors, etc.
Hiding something is pretty pointless, if the process of getting whatever it is to wherever it is hidden, is announced to the entire planet by shooting it into the sky on roaring pillars of fire.
> The moon is also a pretty decent staging ground for the rest of the solar system
The rest of what now?
There is Earth. There is the Moon. There is Mars. This is all the places in the solar system a human could, in theory, visit without immediately dying horribly. Maybe Phobos. Maybe.
The other planets are off limits: Mercury is worse than literal Hell. Venus is a hypercorrosive hothouse. Jupiter, Saturn, Uranus and Neptune would instantly crush everything in their deep gravity envelopes, and most of their moons are highly radioactive hellholes. Not to mention that everything beyond Mars is not even theoretically reachable with a manned spacecraft as of right now.
So, that leaves Mars. A freeze-dried, irradiated, airless, toxic rock desert covered in microabrasive regolith, with too low gravity, no magnetic field to speak off, no available Nitrogen, and no resources that aren't found in abundance on Earth. And before anyone says "Land": May I present the [Gobi Desert][1], a 1.295 Million square kilometers large rock desert, smack in the middle of Asia. And while it is largely a cold, barren rock desert, it is still a paradise compared to Mars.
And even so, the Moon offers ZERO advantage as a "staging ground" for Missions to Mars, because, there is nothing on the Moon to be staged. Every kg of stuff that would be "staged" there, has to be first launched from Earth, so all a Moon Base does, is add another launch to an already costly equation.
[1]: https://en.wikipedia.org/wiki/Gobi_Desert