Plasma weapons are simply better than laser weapons. Does it make sense to spend time and resources on researching and building laser weapons in the mid-game, when you are going to replace them with plasma weapons in the late-game anyway? Especially considering that you can get plasma weapons for free by stunning aliens.
I just played a play-through where I completely ignored the laser tech tree. This is what I found out:
The plasma pistol is not really a priority. It is just a tiny bit worse than the assault rifle (same damage, but it lacks the 10% crit bonus). Its only advantage is that it has infinite ammo. But that alone doesn't make it a serious upgrade. So until you capture your first light plasma rifle, you should rather focus on getting other key techs like better armors, the satellite nexus and the firestorm.
As soon as you encounter the first aliens with light plasma rifles, you should focusing on obtaining as many as possible. Your goal is to obtain 7 units - one for research and 6 for your soldiers. This will be the most challenging phase of the game, because you will be outgunned and because you have to take additional risks to capture aliens alive. But as soon as your research is finished and you can hand your first light plasma rifles to your assault and support soldiers, you will have the playing field leveled.
From now on you can research the rest of the plasma tree without obtaining the alien weapons. When you are lucky, you will be able to finish researching the normal plasma rifle before even finding the first one. But be patient - they are much too expensive to produce yourself. Wait for the aliens to deliver them to you.
Now it's time to farm normal plasma rifles and gradually replace the light ones. You will notice that your heavies and snipers are very underpowered in this phase of the game, because they are still using terrestrial guns, while your support and assault soldiers have already reached the endgame. I would still take at least one squadsight sniper on missions during this phase of the game, but heavies aren't useful right now, so they can stay in the base. Fortunately, you can easily train new rookies in this phase of the game, because thanks to the plasma rifles they will be quite powerful.
The lack of power of your snipers and heavies will change when you researched the plasma sniper and the heavy plasma gun. The plasma sniper must be built, but thanks to not buying any weapons until now, you should have saved up enough resources for that by now. Heavy plasmas can be farmed, but they don't show up before you encounter muton elites. So when you can afford it, you should build one or two.
I don't find the alloy shotgun very useful. Sure, it does more damage, but I still prefer the plasma rifle for my assault troopers, because the better range makes them much more versatile.
if you are playing on impossible and/or iron man consider what class will be your main killer, and then focus on them. i chose sniper (290 kills total on impossible, and hit twice) so i bought a laser/plasma sniper for him and used scavenged rifles for the rest. armor helps if you keep getting bad luck in maps but scopes help even more.
I wouldn't recommend completely skipping laser weapons at higher difficulty levels. If you start fighting large quantities of Mutons/Cyberdisks/Chryssalids with ballistic weapons, you are going to find tactical fights very difficult.
I usually grab laser rifles, but then ignore heavy lasers and precision lasers in favor of moving more quickly to plasma weapons. This makes my snipers and heavies less useful early on, but I think its worth it - just run with more supports/assaults equipped with laser rifles. Snipers are still useful with basic ballistic sniper rifles, and I just don't use many heavies until later in the game.