You want to get to Nonlinear Mathematics, which has two level 1 prerequisites. This gives you weapon 4. You would also want to go for Doctrine: Mobility, which is a level 1 tech. Finally, Industrial Base, a level 1 tech, gives you Synth Armor, which is armor 2. For armor 3, you would need High Energy Chemistry.
Planetary Networks is also an important early military tech. Getting the enemies datalinks is ernormously useful wheen fighting a war. Also you can reverse engineer the standard probe team to get rovers without Doctrine: Mobility (if you are willing to sink that far ).
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