Phasers set to stun don’t kill people, interstellar travelers kill people.
Fairly simple engineering changes could fix those things.
In many ways, guns would work BETTER on the Moon. There is no air to slow the bullet down or change its path, and the bullet will drop far, far less in a lower-G environment. There is never fog of weather or atmospheric blockage of any kind to obscure sighting or laser targeting or rangefinding.
Googling “orbital speed moon” returns 1.022km/s which is about the muzzle velocity of an M-16.
Moon’s lower velocity would allow the use of lower velocity ammo; One of the reasons you want high velocity is to get to your target fast so that gravity has less time to lower the projectile. With less gravity, the bullet will drop less in a given amount of time so you could accurately shoot further (6 times?) with the same setup or use much lower velocity rounds.
Would it be common for the curvature of the moon to make a tactical difference? It already does make a significant difference for air, naval and artillery combat but maybe it would become a factor at smaller scales.
I’d expect to see a lot more good old fashioned shoulder-fired rockets. They won’t overheat, and the lack of gravity/atmosphere would allow them to trade off propellant mass for payload mass, probably a huge mass of suit-piercing shapnel.
But that doesn’t make them stop fighting you. In real life, people can and do continue to fight even when seriously or mortally wounded.
In any case, a spacesuit is more like body armor than a balloon. Both of them consist of multiple layers designed to absorb high kinetic energy impacts. I would also expect these future raiders to wear suits with hard plates much like modern body armor inserts.
Really though, suits would be so vulnerable that I’d expect more combat from armored wheeled vehicles. Wheels could get very large if they don’t need to be solid or inflatable, just large mesh rover-style wheels.
But ------- recoil in low g? You get the (we hope) bad guys and launch yourself to the dark side.
No, rockets don’t really have much recoil at all. The tubes are open.
That’s why we yell “backblast area clear” before we fire them. The tradeoff of not having recoil is having a large burny gas plume shoot out the back.
Perhaps not only as armor, but as ballast. I’ve seen designs for more flexible/lighter pressure suits than what the Apollo astronauts used. I could see how between a more flexible suit, but weighed down by by armor plating, one could be much more nimble on the moon.
How about an elegant weapon for a more civilized age?
… which is the speed at which the moon travels in its orbit of the Earth, not the speed at which a projectile would need to travel in order to orbit the moon.
The values ftg gave, above, are certainly close enough for idle InterWebz Spitballing. I was vastly overestimating the effect a vacuum would have on muzzle velocity (actual effect of removing air resistance from muzzle velocity: “pretty much negligible, although positive and non-zero if you want to get really sticklerish.”) Lunar orbit speed is about 1680 m/s, or 1.680 km/s, or ~3760mph. As noted above, the fastest rifle bullet (Remington .17, I’m guessing) is well below that.
[xkcd]“But … what if we used more power?”[/xkcd]
Well, 1680 m/s is pretty close to the muzzle velocity of a Paris Gun (1640 m/s). Wouldn’t have to tweak that WWI-era technology too much in order to literally fire it around the moon.
Getting something the size of a Paris Gun up to the moon seems uneconomic, but who cares about that when we’re InterWebz Sci-Fi Spitballing?
Changes from conventional firearms you’d need:
a. Dry lubricants since oils will boil in low pressure
b. Design for a greater temperature range - you might need to use modified propellants so they are stable in 200 Celsius lunar daytime. This also may require fancier alloys.
c. Design for vacuum heat dissipation, or just heavier parts so more rounds can be fired before overheating.
d. Armor piercing rounds or bust. Today's spacesuits have some kevlar in them to protect from micrometeorites, this makes pistol caliber and flechette rounds unlikely to even work. So rifle caliber or nothing.
e. Bigger trigger guards, gun cameras instead of sights mounted on the gun, safety levers that can be operated with heavy gloves on - lots of changes.
All these changes might mean the firearm looks hugely different than anything used on earth. But, fundamentally, it’s still just a stick that goes bang and shoots speedy chunks of metal. Also, regular guns will work for a few rounds without any of the above changes, you just might have trouble winning a space gunfight against someone equipped with a weapon designed for the environment.
Also, would you actually have human “infantry” in space? It costs a very large amount of money to put anything into space, and it’s really hard to keep a human being alive much less get them home from a mission. Since it costs a fortune anyway, any cost advantages of human infantry versus various missiles and drones might be zilch.
Given the glove/trigger problem, it might be easier to have it remotely controlled. The shooter might say “Alexa, fire a round … now.” 
You’re probably, almost certainly, right. I’ve only done a couple LAWS and ------ I’m still having a problem seeing me shooting one off in lunar g. Wouldn’t really want to crack off my M1 either though.
Good points. The other difference is that anything that can take out a suit at close range is still lethal out to the horizon (and even slightly over the horizon if you get your trajectory right). Probably affects tactics more than the weapons, but you’d want any gun to have long-range targeting ability. So lots of bipods,etc. maybe even fancy auto-stabilizing devices (since the extra weight doesn’t matter as much)
That’s why I suggest that vehicles are going to be a lot more important than suits. Picture turtle-like vehicles with enormous wire-mesh wheels. They’ll be prone to flipping, so they’ll be armed and armored to fight upside down.
If we actually need to get troops in the base, then the vehicle will be the armor, the suits will be minimal. It will be motorized infantry tactics; get the troops as close as possible to the enemy base. They will fight hand to hand to avoid breaching the hull, because everybody dies if the hull is breached.
More likely it would be an artillery duel though.
That or other smart weapons.
Think about what it means to send a single infantryman. You are sending the mass of the soldier, hundreds of kgs in equipment, life support equipment, you must have some sort of plan to bring them home or medevac them if they get injured.
Or you send 50 small missiles.
On earth, infantry is the thing powers will resort to partly for cost reasons. You can just draft someone, they need in USD about 30k in training and pay to be a basic infantry soldier, with a few thousand dollars of equipment. Equipment that will usually survive the death of the soldier.
Each BMT is 10 million dollars, a modern jet fighter is about 100 million just for the plane. And training is much longer in time and also proportionally more expensive - it costs a lot more to qualify in an Abrams than it costs to qualify with a rifle.
In space, each soldier is far, far more expensive and the same mass can go to a one-way trip robot weapon, whatever is appropriate.
See, I think part of space combat would necessarily include donning pressure suits and depressurizing any structures or vehicles for just that reason. Because giving everyone a pressure suit and oxygen is nothing compared to the cost of getting into space to fight a war to begin with. And if the risk of a hull breach is so obviously catastrophic*, then it stands to reason they’d do more to avoid it, and seek to hobble themselves less, than limit themselves to fighting with spears, particularly when the enemy is probably happy to stand outside and drop a refrigerator on them from orbit before they even know they’re there.
I also think surprise attacks with remotely controlled precision weapons will be the norm. They’re kind of getting that way now.
*As an aside, this kind of “if it would be intuitively obvious to even a casual viewer with a modicum of sense that something can be done a certain way and result in wildly disproportionate damage to the enemy, then there had better be a damned good reason—even if not explicitly stated—why it’s never been done in universe before. If it suddenly is done, that undermines the entire universe” dilemma is why I hate the Holdo maneuver, post-hoc rationalizations in secondary media notwithstanding.
Yeah, I just can’t really see people fighting on the moon. What’s the military objective?
If country A doesn’t like the fact that country B holds certain places on the moon, it would probably be cheaper and easier to bombard it from earth than to maneuver on it from the actual moon.
If country A wants to steal moon stuff from country B, then they would probably maneuver into a position where they could cut power/depressurize/isolate them logistically and wait for them to die.
The weight may be the greatest difference. Normally, soldiers carry about 1/2 to 1/1 of their weight, preferably 1/3. On the moon, a 150lbs soldier who normally has a combat load of 50lbs could use 300lbs. They might end up looking like space marines.
Thanks for the correction.
In such an environment, would guns or rockets tend to make more sense? One of the things that hampers guns is that their highest velocity tends to occur in a high air density zone which slows them down. In space, you don’t have to worry about air resistance or winds messing up your range or accuracy.