The short answer: start with Death and the Shifter and read forward. Anything aside from that is optional context.
The longer answer depends on what kind of reader you are.
The chronological order
Death and the Human comes first in the timeline. It's a novel-length prequel covering how Molly Coyle died in a back alley in Salem, Oregon, and got recruited as a reaper by an angel of death... which sounds like the beginning of a much grimmer series than this turned out to be. It's the fastest way to find out whether you like spending time in Molly's head.
Then comes Chronicles of an Amateur Reaper proper. It's eight books following Molly through her apprenticeship, her complicated afterlife, and a supernatural community in Oregon that mostly finds her exasperating. The series is complete.
Then Chronicles of Molly the Reaper picks up a few months after the first series ends. Molly moves to Dublin with her boyfriend and Fuzzy, leaving most of the Salem crew behind, and starts over in a city where the local factions have opinions about her arrival. It's an ongoing series and a genuine fresh start — you could read it first without being lost, though you'd miss why certain things land.
The order I'd actually suggest
Start with Death and the Shifter. It's book one for a reason, and the prequel works better once you already like Molly (some people do feel that her snark is excessive). Then read the first series through to Death and the Sidhe, which properly ends that story. Then cross to Dublin.
Pick up Death and the Human whenever you're curious. It's free if you subscribe to my newsletter, and offered at a discount if you'd rather skip the email. It works well as either an intro or a look back to how Molly started along her unexpected path, and it reads fine at any point. It also explains a few things that the main series treats as settled background.
A note on how the prequel ended up out of order
I wrote Death and the Human first and then sat on it, because I'd pictured the series being more action-driven and thought the book was too relaxed and too snarky to set the tone properly. Then the actual series turned out relaxed and snarky, so the prequel had been right all along. It came out after book six.
If you're starting today
Death and the Human: free or discounted prequel, read anytime
Chronicles of an Amateur Reaper: books 1 through 8 (complete)
Chronicles of Molly the Reaper: ongoing, starts in Dublin