I found that reading them from the start is the only way that feels right. The first one, 'A Cold Day for Murder', sets everything up: Kate's history with the Anchorage DA's office, her complicated relationship with Jack Morgan, and her deep ties to the Park and her Aleut heritage. Skipping around ruins the slow, deliberate way Dana Stabenow builds her character over time.
Trying to start later, like with 'The Singing of the Dead', left me completely lost on some of the ongoing dynamics, especially with the whole Berger scheme and her grandmother's legacy. The minor characters, like Bobby and Dinah, also evolve book by book. Honestly, just tackle them in publication order; it's not a huge commitment, and you'll appreciate the subtle shifts in the Alaskan setting more.