I feel as if I should write a tactical guide for the aliens one can encounter and what weapons I prefer for them, ordered by difficulty, from least to most difficult.
blood spider:
Attack has a range of only 2 fields, no ranged attack. Hardly manages to kill anything after turn 1 is over. Civilians know very well how to run away from spiders so that they cannot attack them (much better than me). Hard to kill, but can often be ignored safely in favor of more pressing targets, if it's not near to me or civilians. Explosives and sniper rifle seem most effective. Interestingly, the more advanced sniper types seem less effective than the basic sniper rifle with EP ammunition. Seems to need about 10 TUs to attack, so ~30 TUs of movement away from them should be save.
combat blood spider:
Harder to kill and attack deals more damage. Other than that, see basic version.
armored Taman:
Lasers work well. Can move almost 30 TUs and then apply a plasma blade, so ~30 TUs away I am safe.
Ortnok:
Extremely hard to kill. Lasers work well. Has the lowest TUs, less than armored Taman, so still not very effective in killing me or civilians. Making them bleed is a great help, since aliens never use medikits. If one is near my starting position, delaying killing him by flashbanging him can be useful, since I can then use my TUs on more pressing targets and kill several aliens, while I would have needed a lot of TUs for killing just that one Ortnok. This tactic can be applied to other organic aliens as well, but with lesser effect. A plasma blade is a elegant way of killing an Ortnok, the rate of TUs or ammunition needed for that action to get this kill (as opposed to killing with ranged weaponry) is very good.
Hovernet:
Pretty effective in killing me or civilians. Robotic aliens don't bleed, but never use grenades or plasma blades. Sniper EP, sniper or explosives seem effective. In 2.6, (basic or combat) hovernets very well manage to retreat behind cover after firing. This is very problematic in combination with the fact that civilians don't hide behind cover, so if I hide, they kill them. Killing with reaction fire is too dangerous, since even if it works and I do hit, it very likely still doesn't kill due to the damage scaling. Sniper weapons and grenades can hit it while it's behind cover. Seems to have more than 40 TUs, the shot takes 10.
unarmored Taman:
Their TU boost clearly outweighs that they are the easiest alien to kill. I stay away 40 TUs. Extremely effective in killing civilians or soldiers with a plasma rifle.
Sheevar:
Extremely effective in killing civilians or soldiers with a plasma rifle. Can spend almost 40 TUs and then pull out a plasma blade and kill however strong the soldier is (8TUs for taking out and applying). Plasma weapons seem to work best, including plasma explosives, since they never wear armor. Lasers also do. Incendiary grenades are a good idea if I cannot quite kill a sheevar on my turn. Once it's his turn, he will try to get to me, but the fire always deals good damage (no armor) and will likely deal the little additional damage I need. They sometimes walk into their death with open eyes.
Combat hovernet:
I consider these the most difficult enemy now, due to them almost always retreating after shooting. Extremely effective in killing civilians or soldiers thanks to 3 shots with 10 TUs. Seems to be equally hard to kill as the basic version, which isn't too hard though. One hit with sniper EP is often enough on easier levels. Explosives are also good.
For all organic aliens, their difficulty/killing priority also strongly depends on what weapon they are wearing, the plasma rifle is most dangerous (more than any particle weapon - it's more precise and more shots), while a plasma blaster or plasma pistol will often miss when trying to hit civilians or me. If any alien is within movement range of me, it outweighs everything else though (plasma blade!).
This btw means that the campaign is unbalanced - Sheevars should appear after Ortnoks, unarmored Taman after armored ones (lol), plasma weapons after particle weapons.
So, I try to use basic sniper ammunition or sniper EP and explosives against robotic aliens, lasers and advanced sniper weapons against organic aliens. Of course, if it's a high priority to kill that thing or the soldier has nothing better to do...
Particle weapons need a good research time I like to use for other things and are less precise in comparison to lasers. While they deal more damage, alien armor is better against them than against lasers, which takes away some of this better damage.
EDIT 12.09.2020
Corrections to weapon time units. According to base/ufos/otheritems.ufo, (combat) bloodspiders need (10) 12, (combat) hovernets (16) 16 time units for their attacks. So, moving around a little and throwing a grenade is safe while in a hovernet's field of view.