Discard notions of range and damage as proposed in the original Battletech game. Each of your combat machines, even decades out of date and relegated to garrison duty, could trash almost any weapon in the modern arsenal. They are large, powerful, and ultimately deadly machines.
The Shadow Hawk has a shoulder mounted AC-5. This is neat because it means both hands are free to carry another weapon system, like a second AC-5 Wolverine Style. The Shadow Hawk's gun is a long barrel cannon, and as such it has longer range and greater accuracy. Stressor can hit targets accurately at 2-4 miles with this gun. The Wolverines carry snub barrel AC-5s, which are functionally going to be 75mm versions of Submachine guns. Accuracy isn't great, nor is range, but the gun makes up for it in rate of fire, the snub barrel guns can fire multiple times in a combat round. The Hatchetman has the biggest gun with a shoulder mounted AC-10. Rather than going bigger calibre, the AC-10 on the Hatchetman represents a multi-barrel rotary autocannon like on the A-10 Warthog. THe cannon produces a massive hailstorm of bullets that rip mechs, infantry and pretty much everything in front of it apart.
If you can see it, you can hit it. There is no knock-down or knock back from a laser.
Missiles: better for hitting things other than mechs.
All of the mechs in this unit have two functional hand actuators, meaning that they can carry an additional 'rifle style' weapon system. These are compact and self contained, with the Wolverine's AC-5 basically showing what they look like. The Hatchetman can only equip light weapons and retain the use of it's hatchet (AC-2, Medium Laser 'pistol'). If the Hatchetman forgoes the hatchet, it can carry a standard medium sized weapon. The Shadow Hawk can equip medium and standard rifle type weapons, with one cannon over the shoulder, and a second in it's hands. It can carry either a second AC-5, a Large Laser 'Rifle', or a double barrel medium laser pistol. It can also choose to equip a hatchet like the hatchetman.
The Wolverine gets a special note as it can put down it's main weapon system completely. As such, the Wolverine can equip larger weapons than the Shadow Hawk or Hatchetman can (bonus for being a common mech) and this includes sniper style Light Gauss Cannons, heavier AC-10 rifle style cannons, plasma rifles, or over the shoulder mounts like artillery pieces, large bore mortars, and whatever else suitably anime comes to mind.
Drawback: These things have to be requisitioned from the arsenal and approved by the quartermaster and the unit commander.
Is there a mech sized Bazooka? Yes.
Can you have it? Probably not right now.