According to Wikipedia and other sources, Pius X recommended the "Roman" or what we know of as the ecclesiastical pronunciation in a letter to the Archbishop of Bourges, but I can't find a copy of that letter anywhere...
The 'classical' pronunciation is an academic reconstruction from the late 1800s. I've never heard anyone use it outside of a classroom, and it sounds a little grating on the ears. Some teachers get really picky about it, but a priest singing "Gloria in ex-kel-sees Deo" would sound kind of ridiculous, and even then most teachers that use it don't follow every detail of it exactly.
Until Pius X, there really wasn't (and in practice, still isn't) any such thing as the
ecclesiastical pronunciation, so much as a variety of regional pronunciations that more or less reflected the orthography and pronunciation of the local language. (Wikipedia on local Latin pronunciations
The common ecclesiastical pronunciation now is the Italian one, but even today you can hear Polish priests pronouncing Latin C as 'ts', German priests pronouncing Latin GE/GI with a hard (velar) g, or French priests pronouncing Latin U with a front vowel, a
Steer him towards the ecclesiastical pronunciation, but in practice it's always been pretty inconsistent.