Olivares, the Miam Miam Dodo guide has a very complete listing and description of such accommodation. As a winter walker, I had few problems with prices and book-outs, finding perfectly fine rooms for as little as fifteen euros. On the other hand, if your are walking in May more places will be open for the season. I doubt that you'll have trouble with an upper limit of 40 euros.
With private accommodation, one can always ring ahead. My Movistar coverage was strong along the whole
Camino Frances, at least when I checked it. Miam Miam gives all phone and email contacts - though I didn't find that necessary too often in Spain.
The only oddity: Miam Miam provides fewer suggestions for cities, on the understanding that pensions and hotels are so numerous that there's no point in trying to suggest one over another. Still, there are always some private places listed for cities.
The book is updated every year, so buy new. Even though it's in French, the layout is clear and you get very detailed but uncluttered route maps which focus strictly on the track and junctions. (I'm told they're adding some contouring etc to new editions.)
I haven't used other guides, since I'm a hardcore Miamist, so other suggestions on this thread could well be more useful than mine. Worth a mention, however.
Rob