A lot of people label the Vorkosian Saga as military SF but it really isn't.
It is really mainstream character-and-ideas SF with a strong character-driven focus.
The confusion arises because the core character of the series, Miles Vorkosigan is from a militaristic society (for good and valid reasons, actually) and in his younger days is determined to excel in the military (for good and valid reasons).
However, despite the military background, the stories are *not* about soldiers or battles or campaigns.
Some are capers, some are (murder) mysteries, one is a comedy of manners, and all are about human passions and foibles playing out on strange but recognizable worlds.
And because the author is a very good writer with something to say about human nature, they are excellent examples of contemporary SF.
If in doubt, give Cetaganda a try. Or Mountains of Morning.
The novels are self-contained and can be read in any order.
But if you're willing to commit to the full series, just jump in at the beginning; Shards of Honor, and meet Miles' parents and *their* contemporaries.
Very much worth buying and it helps they are available at fair prices and DRM free from BAEN.