This is written for 3.19.1 balance.
The Assault Squad is the most expensive T1 unit in the game and quite powerful. It is very effective against ranged units and especially setup teams.
Assault Marines have heavy infantry armor, which means they will take extra damage from power melee weapons (e.g. Howling Banshees and Stormboyz), but tank ranged fire much better, which favors them in situations where both melee units are being shot at.
Apothecary players will typically get one ASM, while FC and TM players might or might not, depending on the matchup. Getting two Assault Squads is very strong in T1, but the build is very expensive and will probably be countered by a fast walker, which will destroy them.
The starting ability of the Assault Squad, the Jump ability allows them to relocate quickly and knockback normal infantry units. Typically you would Jump on a ranged unit to stop it from firing, but you can also use Jump to stop a melee unit from approaching your ranged units. The knockback from the jump ability makes the Assault Squad a good counter against suppression teams (such as devastators or havoc marines).
When support is limited, it may be prudent to plan for jumping out of a melee as well (instead of retreating and taking increased melee damage).
Thunder and LightningEdit
This is primarily an anti-vehicle upgrade that you get for the Melta Bomb ability when you either have a walker vehicle to counter or want to take out a fast vehicle without investing in a lascannon. The cost of 30 is not insignificant, so don't get this upgrade unless you need it.
The Blind Grenade ability will stun a ranged squad (a suppression team, most likely) garrisoned in a building, allowing you to flame or grenade the building, and it will also stun turrets. This is useful in theory but rarely really effective in practice.
The Sergeant upgrade is pretty much mandatory in T2, the power sword will make the squad kill some heavy infantry models, and the Merciless Strike ability helps a lot against low-health melee units like Banshees or Slugga Boyz but very fun to use vs large groups of Tyranids. You can use it to stop an unit to cap a point. It will make a cool knockback and damage. Also causes some eye-candy for you.
In the other hand, this ability eats 30 energy. When you use it too much, maybe you might not find enough enercy to jump again or to save them from dying. Do not use it in unnecessey sutiations. But, if the squad already leveled up and has a lot of energy, no problem.
The Assault Squad works best with the Apothecary, who will pretty much grant them double health with a well-timed Heal and can also buff them with Combat Stims or give an extra knockback with Purification Rites. The Techmarine offers least synergy, but ASM can be a solid choice with any hero if the situation calls for it.
Also, offensive players likes ASM. That is why in multiplayer most Force Commander players buys an ASM squad. They will help the Force Commander in the front.
Outside hero choices, the Librarian has much to offer an Assault Squad. Veil of Time makes them impossible to kite and allows them to get some retreat kills, which is usually hard for ASM. Gate of Infinity allows you to use the ASM more aggressively and chase the opponent further to get some kills, then pull the squad back with Gate instead of a risky retreat.