UFO: Afterlight wiki
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This is an advanced analysis of trainings for your troops in Aftershock. By its nature, it's very spoilerish. This is your only warning.

It's pretty hard to define the role of your troops based on training as there are overlapped skills. It's better and easier to imagine them base on their most used skills.

Long Range Shooters[]

This is the role of mostly snipers, attack from very very far away, farther than the range of rifles or machine gun. 

Long Range Shooters, as implied, use Long Range skill, shoot Sniper-req guns. The sniper scope has been deleted the sniper requirement in a patch, so scoped guns no longer belong to this category.

The based training is Sniper group, of course. Due to her nature, Psionic has great advantage in following this training: high INT so high Enemy, and easier to advance in both training categories due to overlapped skill reqs. Also, Psionic outfits has many features of use to sniper: cloak collar, life drain/sink for Ultrasonic Sniper, etc... The final finishing training would be Stalker to increase stealth, long range, and enemy. 

Earliest  3/3/3 Psionic/Sniper/Stalker can be achieved at level 11.

A Psionic/Sniper/Leader should be grown for the role of leading the sniping group, with her skyhigh Enemy skill embuing the other snipers with heroic level. Level 15 is probabbly the earliest level you can finish her.

Needless to say that we can grow Human and Cyborg as long range shooters perfectly well as your personal preference. But, this role seem to suit Psionic best, make use of her unique talents and eliminate her weakpoint. Since Long Range Shooters always lagging behind, her low HP and speed is not detrimental to survival.

Rifleman aka Troopers[]

As the name implied, this troop use Rifle skill. He will use Rifle-class guns for most situation, even when using other skills than Rifle in special case.

Since he use Rifle, the base training will be Trooper, even though Rocket equipment class skill use mechanical stat.

A strong variant of this approach is to attach a variety of underbarrel grenade launcher to rifle in order to shoot explosive using Throw Skill with Rocket equipment requirement. This afford the Riflemen another option for the situations that require brute force instead of finessee, such as a roomful of entrenched enemies, or enemies resistant to bullets.

Generally riflemen is strong enough to wear at least medium armor and helmet.

You can use Riflemen as scout, but the rifle shoot slower than shotgun and pistols, so it's of necessity to shoot fastmode, and recognize them first.

Trooper training by itself is enough, and after that just invest in stats that raise Rifle skill, which is one extreme way to play it. Another way is grouped with Gunman class, the which provide two special and useful abilities. One convenient, but not that useful, combination is Medic, what with one lacking stat is very easy to invest, but provide no helpful ability.

Close Combat Specialist[]

There are variants of this type

Variant one: Main combo is Commando Stalker which synergied with each other provide extra boost that is hard to find in other combo. Note that 3rd level of Commando coupled with Katana provide an unique speed boost, and using shuriken/throwing knife/blowpipe has increased crit chance.

Variant two: Melee specialist, the which Cyborg Commando Stalker is the very top. He's stealthy, lightning quick, and slash to the bone. Your Katana wielder is a fearsome sight on battlefield, at least until mid game. require both Close Combat skill and strength stat. Heavy armor would be nice but the key is speed. Get in, slice once or twice, runaway until they lose aims, return, rinse and repeat. shotgun and any quick shooters are the bane of this variant.

Variant two: Shotgun specialist, use shotguns until they can get plasma shotgun. Easily available weapon at the start, shoot fast, a first-blood wounder.  Just Close Combat skill is enough to use this. this is a good counter to katana wielders, as sometimes the shotgun blast is enough to ruin the aims and buying time for second blast. 

Variant  three: dualwield pistoleers. The base training is ranger, then gunman to get heavy armor for protection while getting close enough in range. Pistol is light damage, so they rely on big number of shots to get the job done. Note that in Superhero difficulty, enemies' HP can get bloated to the point of nearly disable this tactic. The first 5-round burst wont disable them, and the returning fire can incapacitate you right away. 

Explosive Shooter[]

I havent found best way to use this. The variant of rifleman and machinegunner use underbarrel launcher to shoot grenades is a nice way, but situational it's not that common.

Manual throw is clumsy. Throw, then get another from the belt, then throw. hold same type of grenades in both hand reduce the time, but still not that much use.

Situational, best one is when you know a close room with many enemies inside, like wargot. In the wide open the nades are of limited utility.

And while smoke grenades, and phosphorus can provide area of effect. it's situational, require one hand, which eliminate rifle or MG shooter.

Machinegunner[]

Machinegunner is a good soldier. Generally they are tough enough to eat a few shots and return a huge volume of fire. With good positioning, a machinegunner can stop a wave of hostiles in their tracks.

There are two variants. Straight up Gunman and a sidejob for technician.

Straight up Gunman is simple. Heavy armor and a modded walking engine of death. Equipped underbarrel grenade launcher ensure that walking destruction get the job done. BUT one thing to remember is that gunman trainings doesnt raise mechanical stat of its own. you need to combine with another trainings to raise it, most notably technician. Its usage is mostly when we need a Machinegunner right away without time to invest in Technician.

Training technician is the proper build to raise Mechanical. In patch 1.3 you have access to heavy weapon abilities in level 2 so you dont necessarily branch back to gunman, but might change to leader or medic, or something else that strike your fancy. Mind you, Gunman training provide useful abilities for machinegunner to be a rockhard steady walking destruction machine.

A quick hire is level4 Cyborg2 you can get early. Due to stat req you can immediately train Technician from that and build from there. Cyborg2 Tech2 can use machinegun by mid-April to deal with Cultists.