My brother and I hemmed and hawed on the issue when we decided to study Latin together. Because the ancient Romans were his motivation, he favored the Classical pronunciation. Because I was more interested in ancient music, I favored the Eccesiastical.
Then we found out that with the Classical pronunciation, Julius Caesar’s immortal words “Veni, veni, vici,” would become “Weni, weedi, weeki.” And we looked at each other in horror and said, “Forget THAT.”
Shallow, but true.
More seriously, I found this blog post helpful in making the decision (though I’m not Catholic).