The Senario: While exploring the bajorian wormhole the federation encounters the empire.
Rules: Canon material only, no temporal interferance.
Timeline: Hight of Empire, just before the battlend of Yavin 4.
Deep Space 9 just before the first encounter with the Dominion.
Additionally: The Q set it up so they will no get involved, expect to annoy significant characters. The rebellion still exists but they are severely weakened as the empire will retask the death star and send a fleet of star destroyers instead. The klingons will quickly join the federation, the Romulus will but it will take time. The Cardassians will ally with the empire.
Some quick notes to help
Empire
Larger fleet, resources, personal, and fighters. Dedicated army. Faster ftl.
Federation and friends
Longer range weponry, more tactical ftl, ftl weapons (this is pre death star 3). Bottleneck on wormhole defense.