This question was asked on Quora recently, so I decided to make a whole article on it. The question is actually somewhat tricky, if you think about it. In most conflicts in history, soldiers of the regular armies were assigned weapons, so their preference was negligible - they had to work with what was given.
Weapons in the Soviet Army
As you may imagine, Soviet Army was just like the rest of the armies at the time, in terms of weapons. Every soldier was trained on some specific weapon system as a recruit. After arriving to his permanent unit he was assigned a so called "personal weapon". The soldier would now be fully responsible for this specific rifle (pistol/machine gun) and he would be held accountable if anything happened to it.
So, in theory, soldiers couldn't choose weapons. They were just assigned with what their commanders thought are the best for the unit. But as always, the theoretical setup rarely stands the test of battle. And this was the exact case with the Soviet-Afghan War.
Personal weapons of Soviet-Afghan war
Small arms of the Soviet-Afghan war were not different to those used by the Soviet Army in regular life. Neither was the battle order of a given unit - especially at early stages. However, what was different is the number of people per unit. Since Soviet-Afghan war was not considered as a war by the Soviet doctrine, those soldiers and officers who were killed, injured or got sick, were not immediately replaced. This created a vacuum in every unit.
Any military man or woman, especially those related to ground troops, know one thing - heavy weapons are more urgent than light weapons. It means, that it is far more important to have crews for your machine guns, grenade launchers and mortars, than to have some extra riflemen. So even a soldier who was trained to be a riflemen or light support weapon gunner could very easily become a mortarman or heavy machine gun operator without any official training or certification.
But of course, not every mission required heavy weapons. And since there were usually more weapons in storage, then battle ready people in the unit, it wasn't rare for the soldier to be able to try another firearm. There are plenty of mentions about this fact in the memoirs, when an officer would say "Just take any firearm you want, but make sure you clean it properly after the mission!"
It is also well known, that support units rarely participated in the actual missions, but would instead stay at the base camps. Yet, these units would have some weapons which could really benefit those on the actual fire missions. Therefore, officers in some units managed to collect weapons across the regiment to improve their battalion capabilities. In this case a soldier, who would usually carry an AK, could easily end up fighting with a PKM or something else.
"Just take any firearm you want, but make sure you clean it properly after the mission!"
Soviet soldiers weapons of choice in Soviet-Afghan war
So now we get to the best part of the article - the list of weapons. Let's start with the basics.
AK-74 with GP-25
This setup was, as mentioned in the memoirs, "the minimum valuable weapon, in terms of firepower". Anything below, like plain AKM or a pistol was considered "unserious". And for a reason. Even though both 7.62 and 5.45 AKs are capable of hitting a target at a range of 300-400 meters, it is definitely hard to strike anyone behind the cover. Given the rocky terrain of Afghanistan, almost any cover was very effective against small arms.
The GP-25 underslung launcher could solve this problem. With the maximum range of 400 meters it was possible to shoot the VOG grenade just behind the foe's cover.
SVD
For precise fire, Soviet Army in Afghanistan would usually rely on the battle module of the section's BTR or BMP. Battle vehicle would be at least armed with 7.62 PKT and 14.5 KPVT, both of which had pretty good daytime scopes with good magnification. This would allow to shoot effectively up to 1500 meters.
However, usually it was impossible to take your BTR with you high up the mountains. And the only weapon in the soldiers' arsenal which was equipped with a scope was Dragunov's Sniper Rifle - SVD.
Of course, in modern world both the SVD and it's standard PSO-1 scope are as outdated as it gets. But back in the 80s, with no other options, this was a really powerful weapon for long range shooting. An experienced soldier could hit his targets effectively at 700-800 meters, which doubled the realistic AK-74 range. So, in most cases, even a smaller unit tried to have at least one person as a designated marksman.
PKM
Crème de la crème of the soviet small arms engineering. There is a popular opinion, that Michael Kalashnikov should actually be praised for the invention of PKM rather than for the invention of the AK. And I totally agree with this.
The PKM is arguably the best general purpose machine gun in the world to this day. While it has exactly the same firepower capabilities as any of its counterparts, it is as robust, reliable and most importantly, light, as it gets. A PKM on a tripod weight around the same as a M240 without the tripod. This tells you something about the machine gun for sure.
And this was surely loved by the Soviet soldiers during Soviet-Afghan war. The powerful 7.62x54R bullet was much better at disassembling enemy's defense positions, than any of the AK bullets. At the same time, with the high rate of fire, it was possible to hit targets effectively at the range of up to 1000 meters. And that's just using the iron sight. For all the reasons above, PKM was widely loved in the forces and a single unit would usually have more of them on operation that it suppose to, by the book.
Summary
In most cases, it was up to the unit officer to choose the appropriate weapons for the mission. But since such an officer would be with his soldiers on such mission, he rarely made mistakes by taking wrong firearms to the battle. And he would usually listen to more experienced soldiers.