The GPU is a large team/small army (approx. 4,000) of mercenaries that work together to complete missions. They do their best to select missions that are considered "good" and have a good reward. There are four larger mercenaries who work together to lead the GPU. They are known as SAPS, an acronym for their code names: Soldier, Aggressor, Punisher, and Storm. Nobody knows their true names.
The GPU has created a separate fleet of ships, known as the Overdrive series. They use higher level technology than standard ships (Archon's Plasma Mod). The Overdrive ships are typically faster and have more firepower, but are more expensive.
Note: The Shipyard can be found here. This one's not going to be updated.
Common Ships:

Name: Laser Fighter
Cost: 114,000
Capable of FTL
Effective in groups, easy to use, and not as expensive.

Name: Missile Fighter
Cost: 137,050
Capable of FTL
Although harder to control, has much more firepower than the Laser Fighter. Also likes to be in groups.

Name: Support Fighter
Cost: 124,450
Weak on it's own, stronger when paired with other ships.

Name: Probe
Cost: 104,775
Capable of FTL
A very light, unarmed ship with a sensor.

Name: Trainer
Cost: 86,300
Capable of FTL
Used mainly for training and testing for admission. It looks like the designer had a brain fart and put PD on it.
Less Common Ships:

Name: Laser Carrier
Cost: 1,066,800
Capable of FTL
Almost completely unarmed, but can create extremely cheap "fighters."
Civil Ships:

Name: Light Cargo Transport
Cost: 118,100
Not created for combat, but designed to take a few hits.
Special Ships:

Name: The Soldier
Cost: 516,050
Capable of FTL
Soldier's preferred ship. Is most maneuverable out of SAPS' ships and can gather information the fastest.

Name: The Aggressor
Cost: 1,818,100
Capable of FTL
Aggressor's preferred ship. Fairly durable and can "drill" into ships.

Name: The Punisher
Cost: 2,396,000
Capable of FTL
Punisher's preferred ship. Fast, strong, vulnerable after first volley, and lumpy-looking.

Name: The Storm
Cost: 3,835,700
Capable of FTL
Storm's preferred ship. Like The Punisher, but volatile and with missiles.
Things that aren't ships:
Note: Huge ships mod required.

Name: Large outpost
Cost: 7,468,200
Capable of FTL, for some reason.
Good place to seek cover and repair, but struggles with rotating.