I mean you could probably start by wondering about your alien race's relationship to their tools and weapons are. On Earth, it used to be common for people to have their weapons named and personalized as a way to demonstrate status - do they do the same? Do the aliens have similar or completely different notions of property and status that we do? Does an alien get his first plasma blade from his father after he's completed thirteen solar rotations and is eligible for the mating cycle? You might also ask who builds them, and why. Of course, all of this is only if you're interested in that kind of "sociological" world building - it's totally fine for an alien to be wielding a Plasma Fucker because it's cool and the bad guys need weapons to distinguish them from the goodies.
I think though that truly iconic weapons tend to be strongly rooted in place and setting. The lightsaber is like an archetypal example of that; it's a cool visual element but it is also symbolic of the character's development within the story as like a milestone of their progression. Also, a weapon can tell you about the attitudes and norms that are typical of the wielders - remember how cavalier they were with nuclear weapons in Starship Troopers?
Further, you could think about who gets the heavy firepower and who does not. At the end of Disco Elysium, the two protagonists have to face down a gang of private corporate mercenaries who are armed with anti-tank weapons and space age body armour. The protagonists are under-funded police officers with flintlock pistols. Without drawing explicit attention to it, the narrative demonstrates what kind of society these characters are living in.
Also, I love the idea of living ammunition, you should add a gun that fires an armoured egg that dissolves in the target and releases a swarm of parasites that devours them from within.
Asphyxiant capsules: Covert, nonlethal, can be thrown or fired as ammunition depending on their design. They'll break up on contact and release a splattering of chemicals that easily spread through the target's skin mucus and react with it, making it difficult or impossible for the target to breathe through their skin. Not much of a concern on its own, but this really fucks with amphibioids attempting to hide from the authorities underwater, run long-distance, and other ordinarily anaerobic activities that could be better sustained by, y'know, having all your extra breathing surfaces available. It doesn't really do much to humans, who do not have an amphibious mucus, but we are pretty watery and bare-skinned creatures, so it probably tries its damnedest to do something anyway. Can leave a tenacious, shoe-polish stain in your skin and smell equally bad. It probably really sucks to get in your eyes, because it spreads naturally through liquid mucus, and amphibians generally have protective eye lenses that humans do not. The chemical itself is relatively biodegradable and will dissipate after a few days in water- I imagine that high-tech, industrialized amphibians would have a huge taboo about chemicals that don't decay quickly naturally, considering amphibians on our planet are often the first to get horribly affected by chemicals in the environment. They would probably have the same lingering persistent fear of anything that makes toxic chems that we do about any technology that's radioactive.
I also think amphibians would be far more likely to weaponize plasma than lightning and rays. Amphibians as a general rule are a pretty conductive bunch when they're on land, and they're also pretty difficult to hit, from a lightning bolt's perspective, when they're under the water. Ever wonder why dead fish don't start floating up in the hundreds when lightning strikes a boat and goes down into the lake that it's in? Because water in nature is pretty conductive- More conductive, even, than all the bodies swimming around in it. It's not exactly safe, but water almost creates a kind of faraday cage in the fact that it's conductive enough that lightning sort of actively seeks it out, and most creatures are pretty much made out of water with a bunch of shit in it, which is often not as conductive as normal water is. (Although water does need some shit in it to be conductive. Water completely on its own is an insulator.) Particularly slimy individuals might have a modicum of protection in that voltage might prefer to travel through their slime and over their skin rather than through their skin and organs, and individuals firing these things in water may well be in more danger than the people they're pointing it at, because lightning disperses pretty well in all directions when it hits water and doesn't affect most things under the surface because of this effect. So a lightning gun under water would probably just create a small, melee-range invisible cloud of harm in front of wherever it fires at best, or just electrocute the dude who shot it at worst. But I suppose this isn't really an issue because lightning gun implies you figured out some anomalous science in the first place in order to get it to fire in a particular direction rather than just flail around for the path of least resistance immediately, so more power to them I suppose.
A plasma beam, while also electric in nature, can keep most of the conductive and charged components insulated within the gun as it fires out superheated meat-melting sparks of death. The plasma gun is probably most attractive to an amphibious race because, unlike heat rays, lightning guns, and ballistic projectiles, superheated plasma is probably pretty comparable in how deadly and consistent the projectiles are both in and out of water. Lightning disperses in water, rays of just heat will start to make the water around you mighty uncomfortable after too many shots, and bullets lose their lethality beneath the surface at embarrassingly short ranges. But a concentrated bolt of condensed blue fire will be capable of burning your insides for as long as you can still see it, and then there's probably a range where it'll still sting and scald skin. Its range probably still diminishes in water, but because no one has invented the star wars blaster yet and tested it, the suspension of disbelief remains unblemished if you still allow it to have pretty wide range underwater as well.
But I don't actually know that much about plasma or electricity, so anyone is free to correct me on this shit if they want. This was a fun thought experiment, but I'm going to sleep.
I would also like to point out that if they have gotten to a point where space travel is practical, they would need a weapon that reflects that. It would need to be a weapon that could be fired in a spacecraft without doing significant damage to walls and sucking everyone into space.
That reminds me that The Expanse is the only sci-fi I've seen on TV that actually accounts for that. Their equivalent of MAD is that Earth and Mars both have the technology to push an asteroid into each other's gravity well easily and wipe out the entire planet.
a weapon which shoots a kind of chemical spray/slime which is like acid to the chemical compound of the species' own skin. Because if humans create weapons specifically to kill each other aliens can too.
If advanced enough to do pinhole wormholes or molecular compression you could have thrown devices that gate in a huge quantity of water, flooding a room or area, creating a favorable fighting/working area for amphibians and hazardous conditions for other lifeforms. Inherent bacterial life form organic water seals at leakpoints.
Bioengineered entangling kelp grenades.