Which Books Do I Need?
In any case, you will need the Field Manual, as it contains the most recent version of the rules for actually playing the game. Thankfully, it comes with any of the major books (Locked and Loaded or Return to Cat's Eye) if you buy the PDF versions of the books.
In order to choose your army and make an army list to a particular Threat Value (usually abbreviated 'TV' - a points system based on unit effectiveness), you will need additional rulebooks depending on which army you want to start:
Locked and Loaded (version 1.1) will let you make the following armies:
North
Northern Guard
Norlight Armed Forces
United Mercantile Federation Army
Western Frontier Protectorate Army
South
Southern Republican Army
MILICIA
Humanist Alliance Protection Force
Mekong Dominion Peacekeepers
Eastern Sun Emirates Guard
Peace River
Peace River Defence Force
Peace Officer Corps
Port Arthur Korps (updated in Perfect Storm, below)
Leagueless (the perfect army for those who can't choose an army)
Return to Cat's Eye will let you make the following armies:
Caprice
Liberati
Corporate
Black Talons
CEF (Colonial Expeditionary Force - from Earth, or specifically the New Earth Commonwealth)
Shattered Peace will let you make an Eden force. To add CEF elements, you'll need Return to Cat's Eye as well.
Terra Nova Gambit will let you make an Utopian force. To add CEF elements, you'll need Return to Cat's Eye as well.
Perfect Storm will let you make the following armies:
NuCoal
Choose a type of regiment:
Infantry Regiment
Gear Regiment
Tank Regiment
Airborne Regiment
Spec Ops Regiment
Then choose a city-state:
Port Arthur
Temple Heights
Lance Point
Fort Neil
Prince Gable
Erech & Nineveh
Khayr ad-Din Army
County Militias
Port Arthur Korps
Some armies can be combined subject to rules in their respective army lists:
A Caprice force may take CEF or Black Talon units in their army (but not from both), but must fill all compulsory 'slots' with Caprician units.
A CEF force may take Caprice, Eden, or most Utopia units in their army. To do this, you will need the book in which the desired units are listed.
A Black Talons force may take Caprice, Eden, or most Utopia units in their army. To do this, you will need the book in which the desired units are listed.
A NuCoal force may take up to 1/3 of its points value as Humanist Alliance units (see under South above).
OMG, How Do I Choose An Army?
The best approach, at least as far as I've seen among new players of any miniature wargame, is to pick the models that look the coolest to you. You've got to put together and paint them, so you're going to want to like looking at your models for hours on end, and stay excited about how cool they look until you're done building and painting the army. Another approach, especially if you've played and are already a veteran of Heavy Gear Blitz or another wargame, is to look at the rules and determine which army best suits your play style.
For example, I liked the idea of an army made entirely of Striders (non-humanoid piloted war machines, with from two to six legs) and hovertanks, and didn't want to play as the 'bad guys' (the CEF). So I settled on the Humanist Alliance, which allows you to take Striders as Core choices and unlocks a unique model of hovertank that only they get. Awesome!
Another example. After I finished building my 1000TV Humanist Alliance army, I decided I wanted to paint more Gears, but also wanted to be able to use some of my Humanist Alliance stuff from time to time and get some even newer hovertanks (drools over the Fusilier). So I've started collecting a NuCoal army.