Harvest when you can. In Utah, the Utah, Western, and more rare Alligator junipers usually don't seem to carry much water in them at any time of the year, and I've never had trouble drying it that I remember.
Trunks are often twisted and have a ton of branches. I got my best staves by finding big, old, spreading trees, with long branches that grow close to the ground. These branches have been growing under the shade of the branches above them for a long time, knot-free, and reaching out from under growing longer and longer.
The same rules apply; you'll look at a lot of trees before you find one branch, but when you do, you can take the top side of that branch, and often a piggy back stave that can be backed with wood or sinew, without killing the tree. I have even cut partway through the branch, at the tip and tail of a stave, and bent down the limb, splitting the stave free.
