Prioritize protecting your head and torso. Keep an eye on the coverage percentage of various wearable items. I’m guessing some of the bullets bypass your armor completely when you get bursted due to less than 100% coverage. An empty MBR vest, fitted and reinforced, is quite optimal for torso but not perfect alone. Do wear multiple torso items. You really don’t want to rely on just one layer of armor if it gives less than 100% coverage. Personally I don’t go above 40 encumberance, except head maybe.
Do you often get bursted to death down in the labs? You might want to maximize your speed. Note that ‘speed’ can mean aiming/attack speed or movement speed. Use a fast-to-aim weapon on top of having low encumberance on arms, legs and feet. You have be able to aim faster than the turret. Use appropriate sights on the weapon. You can also inspect the effects of encumberance on various body parts in the character sheet. Use TAB and arrow keys to browse. Also wait 2-3 turns behind any lab door before opening it. That restores your speed to full, maximizing your chances to get a jump on anything that’s behind there. A shotgun is good for labs although sometimes the turrets are out of range. An assault rifle or an SMG with burst fire is great. Really annihilate the turret. Also consider running instead of walking through the doors.
A far more safer method to deal with lab turrets is to use a control laptop, which can take over hostile robots, including turrets, even behind a wall. Open door, see turret, close door, hack turret. You can even deactivate the turret (by walking into it) and pick it up along with its ammo. Probably all turrets in the labs are 9mm so why not bring a 9mm SMG, too!
Military outpost turrets are a pain in the ass. I just snipe them, and afterwards possibly use the buildings as cover to approach, and then apply the control laptop.
Roadblock turrets - snipe. Although if you have curtains on your vehicle’s windshield, close them to block the line of sight, drive closer and attempt hack. The other turret might shoot the hacked turret though. Or ram them with the vehicle.
NPCs can be a PITA, too. Be aware of what they are armed with (guns vs. melee). NPCs can soak a ton of damage (used to be a bug, still might be) so don’t be afraid to burst, or use fire or tear gas. Ram them with a car (spiked plates or shredders in front).