What do the three API bars do? I can't get the manual to open so I don't know if it's in there. I assume they stand for something like adrenaline/perception/intelligence? I also notice that if you move the top one (the red bar) to the right in makes your agents run faster, and to the left it seems to make them regenerate damage faster. What do the others do?

I also seem to remember making all bars go to the right setting an agent to 'panic mode' where their AI takes over and starts shooting at any threats nearby. It's been a few years since I played.

Yeah, API = Adrenaline, Perception, Intelligence

Adrenaline:
Left = faster healing but reduced movement speed
Right = The opposite, slower (if any) healing, increased movement speed

Perception:
Left = Can shoot at multiple targets at the same time at the sacrifice of reduced accuracy by scatter shooting the area. (use it with a mini-gun and you'll notice the difference)
Right = Better aiming but can only rapidly shoot 1 target at a time.

Intelligence: (not really noticed much with this)

Clicking down both mouse buttons activates Panic Mode, which activates the auto-shooting, sets everything to the right and auto selects your most powerful weapon in your inventory.

Just a couple notes to add to Lenriak's helpful post:

The intelligence booster drug makes your agents more autonomous, so they will take shots themselves. Maxing their INT drug levels and letting the agents shoot instead of shooting yourself via right click saves a lot of ammo and allows your agents to fight multiple fronts at the same time.

The manual mentions lowering INT allows you to send agents to their deaths, I am guessing the agents were meant to be more autonomous in the design phase of the game and this just didn't make it into the game. You can always send your agents to their deaths, their morale never breaks. (The manual also mentions the agents gaining experience with the weapons they use for example, which is not in the game.)

The panic mode is very, very useful.
As far as I know Lasers are the top priority pick (not Gauss Guns). Miniguns are second to Lasers and are picked over everything else.

Thanks to both of you. I'm finding panic mode very useful, as well. Some missions I just park my agents in an open area and let the enemy swarm to me as my guys effortlessly nail them with miniguns. I don't think I ever gave lasers a try when I first played way back at release, I'll have to have a go with them.

Kind of a related question, what do the heart and brain mods actually do? I know the brain mod makes persuasion easier by lower the amount of 'points' you need to start persuading cops and agents, but I don't know if it increases accuracy or reaction time or anything. And the heart, the text seems to imply increased endurance of some kind. Does this mean greater health, or longer use of API chemicals, something along those lines?

I never really knew when I was younger what bionics mostly did what and I have still to confirm it now, I think the heart also effects the speed you regenerate at (natural hearts don't heal, only bionic ones do) which is also modded by the adrenaline bar.
With Chests they offer reduced damage taken and the ability to self destruct (either ctrl+D or Alt+D, never used kamikaze tactics :P )

Only mark II and III chests have the self-destruct ability.

With Heart V3 you can keep your agents sprinting for a long, long time. The adrenaline drug decays very slowly.

I immediately researched Heart V3 before anything else, and installed Heart V3 and Chest V3 asap in my four main agents before spending money on anything else.

It's almost like cheating. >_>

Every mod is important later because some of the missions are very tricky. Last time I ignored researching arms and went for chest - I could carry only 1 minigun with arms V1 and more of them reduced my speed.

And if you think having V3 is cheating, then try finishing mission at the centre of the ocean (atlanta or sth). :D

Atlantic Accelerator? Not neccessarily.
You need one agent with V3 legs/heart and at least v2 arms, v2 or v3 chests on all, 3 agents (but 4 will do fine). 3 or 4 Energy Shields each, 1 flamethrower each except for the 3rd agent (who needs 2).

Turn on the energy shields at the start, wait until the enemies come closer, switch to controlling #3 and run behind them . They'll keep firing at #1 and #2, so have #3 switch to the flamer and torch them. Repeat same basic strategy for most of the map, except for last enemy agent running in circles inside a warehouse (you have to come to him, unfortunately). The guards with Gauss Guns will not fire at you while you have your shields up.

I found by accident that the last agent in the Atlantic Accelerator mission (the one that paces around in the building) can be killed by using a flamethrower from outside the building (by the door) and hit them as they pass near the door.

The Perception Value influences the spread of shotguns too.

Left for high spread, right for tight shots.