Schools- Explosive, Projectile, Prototype
Houses- Small, Large, Siege
Exp/Small- Grenades, grenade launchers, light flamers
Exp/Large- Rocket launchers, det packs, heavy flamers
Exp/Siege- Mortars, mobile artillery, air strikes
Proj/Small- Pistols (single/akimbo), single shot/semi-auto rifles (non-scope)
Proj/Large- Automatic rifles, shotguns
Proj/Siege- Scoped weapons, recon abilities
Proto/Small- Energy pistols, EMP grenades
Proto/Large- Energy Rifles, light railguns
Proto/Siege- Large railguns, target painting
The School of Explosives is limited in its mobility because of the wait of its weapons' weights, but has more flexibility in weapon choices.
The School of Projectiles is lighter and faster, with easily maintained weapons and reliable damage.
School of Prototypes is tactically efficient, high damage, but lower rates of fire on single targets, particularly effective against robotics.
House Small is quick and personal, they sneak behind enemy lines or attack up front.
House Large is good for laying down suppressing fire at a distance or quick bursts of heavy damage up close.
House Siege is good for long range attacks and command abilities.
I dunno, that's my take on how it could work. I'd imagine you are proficient in all weapons belonging to your school, but get significant bonuses to those of your House.