The Liaden Universe is a set of stories, not a series as such.  So this isn't in any way The One True Reading Order, since there are different arcs and sequels ... plus some of the books overlap in chronology. 

I've noted entry points to the Universe (that don't require prior knowledge) as given by the authors, and also where books are part of an internal arc.

Visit korval.com for the authors' own thoughts on various ways to read and places to start within this universe.

Necessity's Child is the only standalone -- perhaps a good place if you just want to sample the writing with no other commitment.