In my opinion Driller's Job/Playstyle is

As Driller is one I play the most
it annoys me when people barely use their Drills.
You have Drills for a reason...

I try to think what would be the easiest way to go
and what would be easier for my Teammates.

I try to drill pathways to places & just make things more accessible,
to like objectives, supply pods or to get up to/from places.

You can also tunnel under to team mates to revive
or even to kill/hack enemies.

As well as even out the terrain for the team so it's easier to move around.
You are expected to drill around and make space around things
like the Hacking Pod,Fuel Pods etc.

I am also always on the look out to get the buried Gems.
Like Bittergems,Compressed Gold, Jadiz, etc.

In my opinion Engineer's Job/Playstyle is

As an Engineer you basically place Cheese/Platforms,
around and under minerals for mostly the Scout to get to.

You can also place the Platforms to plug holes in the roof or floor
and to get over stuff like Sticky Goo or Lava Craters.
You can also build shelter and pathways.
Speaking of Pathways you can path/funnel enemies
with the Bug Repellent Modification.

turrets - don't forget to place down your Turrets.
In game there's basically stop/break points
where you can set up your turrets,
like during Egg Hunt missions whenever you take out an egg
there's a chance to have a swarm incoming.

Speaking of swarms The SSG(Swarm Shredders) Grenades
are basically one of the best grenades in the game right now.

In my opinion Gunner's Job/Playstyle is

Like always it depends what type of mission.

As a second main, I try to think like a bodyguard
as the last one in the Drop Pod
or last one in the Driller hole to the Drop Pod etc.

I typically try to stay by the Mine Head or The Refinery while having Ziplines up
Trying to cover other Dwarves Depositing or Mining.

But if it's a break from bugs
I try to gather Minerals/Objective to get it done quicker.

Again the way i tend to play is to think of the team.
I like to try and frequently set up Ziplines which i think would be useful.

like in Dreadnoughts fights and fighting in spawn/start room
I try to cross them and have them high enough to dangle above.

In my opinion Scout's Job/Playstyle is

to light up the caves with his flare gun regularly,

the one mainly gathering minerals.
At the very least hard to reach ones.

to be agile enough to escape death

and to be the team medic when the team eventually goes down.

Other's suggest as well to look for High-Priority targets.
Like Mactera, Stingtails, Septic Spreaders,

Since I don't play Scout all that much,
as it's mainly single-target damage and you have to be agile,
I am not really sure of the builds, just things I like.

I like his Grenade Voltaic Stun Sweeper and the Cyro grenade.