An old Army motto goes "one man in logistics counts as ten in the field", meaning that inadequate resource allocation spells doom for an army, no matter how big. That also means that the logistics are the flesh and blood of an opponent's capacity to wage war.
Supreme Commander does, however, simplify logistics, simply because units do not need any kind of supply, no ammo narrowing it down to mass and energy production along with the occasional refueling for aircraft. So, prime and obvious targets are Mass Fabricators, Mass Extractors, Power Plants, and Factories. Less obviously, also Radar, Sonar and Stealth Field emplacements are eligible for logistic strikes, since they do not directly impact the opponent army in the field, but damages it in the medium-long run by denying reinforcements, intelligence or stealth.
One exception to the "no supply" rule is mobile shield generators, which can act as a disposable source of hit points. Since these also regenerate, the situation is somewhat more complex as this fact softens their use as a unit health supply chain. Nonetheless, since these are often primary targets as well as extreme force multipliers in battle, maintaining a steady flow of shield generators toward the front provides a rather extreme advantage (see the Shield Generator Warfare article elsewhere on this wiki.)
Eliminating Mass Fabricators, Extractors, or Power Plants will hurt an enemy's ability to build or repair units. In some cases, experimental units need constant supplies of energy and mass to function. Additionally, T3 Power Plants might explode to cause a chain reaction — an unintended, but welcome, consequence.