If you need more specifics, I'm interested in the 1400s and 1500s, and in the regions that eventually became Protestant (so mainly northern Europe and England). I'm aware from my studies of religious history that the interactions of these two types of "power" were sometimes hostile and sometimes accommodating (and sometimes both at the same time, by the same people). However, I'd like to spend my money wisely and get the best book on the subject.
Medieval or religious historians, what are your recommendations?
The two classic studies are Stuart Clark, Thinking with Demons: The Idea of Witchcraft in Early Modern Europe and Kevin Thomas, Religion and the Decline of Magic. However, these focus more on the early modern end of things. Richard Kieckhefer's Magic in the Middle Ages focuses a little earlier and might interest you.
Right now, medievalists Nicholas Watson and Claire Fanger are working on a project on John of Morigny's Flowers of Heavenly Teaching, a wild fourteenth-century text that describes John's foray into dangerous magic and his attempts to recreate a divinely-based one. Fanger has published Rewriting Magic, which is a study of the text, and she and Watson published an edition (in Latin) together. I believe they are working on a translation, per a conference paper I heard, but I'm not sure what its timeline for publication is. Rewriting Magic is a fairly quick read (it's short) and utterly fascinating. It's very focused rather than being a broad overview, but it might be a good place to start.
Note that the focus is "learned" magic/sorcery and not more folkloric beliefs.