My preferred reading order would be:
Local Custom (Er'Thom & Anne's story - Shan as a child)
Scout's Progress (Daav & Aelliana's story)
Those two give you the story of the parents of the major characters in the rest of the books. They also set up the nuances of Liaden society and how it differs from Terran, and introduces you to Clan Korval.
I would next read the following, because it introduces the Department of Interior story arc:
Conflict of Honors (Shan's reintroduction, Priscilla's introduction)
Agent of Change (introduction of Val Con (Daav's son) and Miri Robertson - introduces the story arc of the Deptartment of the Interior)
Carpe Diem (continues the story arc of Daav, Miri, DOI, Shan, Priscilla)
Plan B (continues the story arc, reunites all the main characters in one location)
I Dare (focuses on the parallel story of Pat Rin, cousin to both Shan and Daav, and the attempts of the DOI to suborn him and what he does about it - and takes the whole crew back to Liad to a showdown against the DOI)
I would then recommend Crystal Soldier
and Crystal Dragon
(in that order) because it tells the backstory of Jela and Cantra not to mention Clan Erob and The Tree. These two books fill in the historical gaps and provide "a-ha" moments. You could probably read them first, but I like to place them after the main story arc because there are constant references to Jela and Cantra in the other books so you already have a sense of their importance. The Crystal books humanize them and give you facts about the Liadens, Terrans, and Yxtrang that connect all the dots that you've come to think might be connected.
Balance of Trade
is a stand-alone, one that takes place after the time of the Crystal books but before Local Custom. It doesn't focus on Clan Korval at all. But you will recognize bits and pieces of things (and possibly people) that have carried through time from the Crystal books. I read it before the Crystal books (because they hadn't been published yet) and when I re-read it after them, there were a lot of "hmm..." moments for me when I recognized what certain things were.
Mouse and Dragon
can be read after Scout's Progress
if you like, because it continues the story of Daav and Aelianna, but I prefer it as a stand-alone after the main story arc.
start a new story arc involving Theo Waitley, introduced at the end of I Dare
Check out Liaden Universe on Wiki, and http://www.korval.com
These books are definitely keepers for me, and I've got them in hardcover whenever I can. I re-read the entire series every year or so. There are also two books called the Liaden Universe Companion
volumes (I & II) which contain the short stories (chap books) that the authors publish yearly set in the Liaden Universe which provides further backstory and tells the tales that get a brief reference in the novels themselves. (If you enjoy the series, I'd get the available LU Companion Vol. II now while it is both available and affordable - Vol. I is out-of-print and costs in the hundreds now.)