Stargate SG-1 (1997)

The friendliest way into military science fiction. SG-1 is a team run out of Stargate Command, a top-secret US Air Force base, and most of the main characters are airmen in authentic Air Force uniforms. The Air Force worked closely with the producers, and two real Chiefs of Staff appeared as themselves. It's more mission-of-the-week than grinding war story, with humor in the briefing room, but the chain of command is always there. Ten seasons and 214 episodes means you can dip in for a long time.