<An interesting problem. How easy or difficult would it be to shoot down a ship on it’s way from the earth to the moon? The orbital mechanics is not that simple. Seems like if your people were looking out for you they could steer you away from the attack. However high a energy beam or laser weapon is another thing. Depends on where it is and how far it has to shoot, and how much energy it can put on your spacecraft. Remember none of this scenario is likely for at least 20 years, so who knows how advanced energy weapons will be by then. I have a feeling we will all be surprised at what is developed.

A particle beam or other directed energy weapon would be best, with the huge advantage of being able to operate totally in a vacuum, which would make the design of such weapons much easier than Earth-based weapons of this type.

A missile would work, but not that well unless it had a pretty active terminal guidance system. A purely ballistic shot could be easily dodged or intercepted by the target since it could be seen coming far away and would also be a sitting duck. Dodging on the part of the target is an expensive proposition in terms of propellant use, but then so is a terminal steering system on a missile (no air for fins.)

A cloud of debris fired into the orbital track of the target would also be effective, but if detected at a great enough distance, might still be dodged.

You could wait until your target landed, then hit it with a long-range mortar. On the Moon, mortars can be VERY long range.

The war could get quite tricky. An attacker could send warheads on ballistic translunar trajectories that used "stealth" technology to avoid radar detection. Lunar facilities, it should be noted, are also sitting ducks.

If I had to defend deep space facilities, I'm afraid eventually I would have to set up a blockade at Earth to keep any rockets from leaving orbit. As with antimissile systems, the boost phase of a Moon launch is the most easily trackable.