Part 1: Background
The game runs with the assumption that the player has seen the prequel movies up to Episode 2: Attack of the Clones (Episode 3 wasn't out yet when Republic Commando came out, but RC acts as a lead in), so if you haven't, the game, especially in the beginning, will lack any context and will be mighty confusing. As it's a very fast game full of shooting, rather than bog the videos down with too much text or long breaks to explain things, here's the story thus far. I'll try to keep it more focused on the political side of things rather than on the main characters of the movies, however, as while the characters may have triggered these events, the game isn't about them.
The Invasion of Naboo - 32 BBY
Despite quickly growing in both wealth and influence amongst the Galactic Senate, the Trade Federation headed by Viceroy Nute Gunray has grown increasingly frustrated with Republic legislation that would weaken and slow the growth of the Federation and would, instead, increase tax revenues to the ever weakening Republic.
With urging from Senator Palpatine in the guise of Darth Sidious, the Trade Federation uses its vast droid armies and fleets of disguised battleships (both of which are presumably meant to combat piracy) to blockade the small, prosperous, and far flung world of Naboo under the assumption that it would fall under the influence of the Trade Federation without incident.
Things don't go according to plan for the Federation when the queen of Naboo, Padmé Amidala, is able to maintain communications with Coruscant and is able to contact Nabooian Senator Palpatine to request assistance. In response, Supreme Chancellor Finis Valorum and the Jedi Supreme Council dispatch the Jedi Knight Qui-Gon Jin and his padawan Obi-Wan Kenobi to negotiate with Federation forces.
Negotiations break down when, under orders from Sidious, Gunray attempts to assassinate the Jedi and the Federation droid armies invade the planet. No more Republic assistance ever arrives and Naboo, with aid from the Gungan natives of Naboo, fights a costly battle to liberate themselves from Federation occupation. They do succeed when a nine year old Anakin Skywalker (goddammit, George) is able to destroy the droid control ship.
Despite four hearings before the Republic Supreme Court, Nute Gunray remains viceroy of the Trade Federation. The Republic orders the Trade Federation to largely disarm and reduce its droid armies. Chancellor Velorum is removed from office due to a vote of no confidence and Senator Palpatine is voted in as supreme chancellor of the Galactic Republic.
Jedi Master Sifo-Dyas, possessing the gift of precognition, senses dark times ahead for the Republic and travels to Kamino to commission the construction of a large growth accelerated clone army without the knowledge or approval of anyone in the Jedi Order or the Galactic Senate. The Mandalorian bounty hunter Jango Fett is chosen as the genetic template for the clone army and agrees in exchange for the sum of five million credits and one unaltered clone for himself that he names Boba and raises as a son. All Republic and Jedi records of Kamino are erased.
The Separatist Crisis - 22 BBY
Opinion that the Republic was growing weak and impotent had been spreading for many years, and the Republic's inability to do anything during the Naboo Crisis only helped to accelerate dissent among Republic member worlds. Despite the Republic's orders following the Trade Federation's failed conquest of the Republic world of Naboo, the Trade Federation has been rebuilding and expanding its droid armies in secret droid and weapon foundries owned by Baktoid Armor Workshop on the world of Geonosis.
Charismatic former Jedi Count Dooku begins the formation of a separate government body to the Galactic Republic, the Confederacy of Independent Systems, and quickly lures in many of the galaxy's largest manufacturing and monetary organizations with promises of free trade zones. They quickly form the Separatist Council and are summoned to Geonosis to formally pledge themselves to the separatist movement.
After an assassination attempt on Senator Amidala, Kenobi tracks Jango Fett to Kamino, rediscovering the clone army, and then to Geonosis, where he discovers the presence of the droid foundries, the presence of the Confederacy leadership, and the involvement of Viceroy Nute Gunray in the attempt on Amidala's life.
He transmits this data to Anakin Skywalker, who then forwards it to the Republic, but Kenobi is captured in the process. Skywalker and Amidala attempt a rescue, but are also captured. All three are sentenced to death by the Geonosian Sun Fac for acts of espionage.
Tensions between the Republic and the Confederacy have reached the breaking point, and a Jedi strike force is dispatched to rescue the three captives. The clone army, the first standing Republic army in a thousand years, is mobilized.
The Battle of Geonosis begins.