Ah, is Lingva Latina the one with Caecilius and his family? I had a Latin class in 7th grade and remember having a book of that same name, and I somehow remember the main father character's name. They had a dog too, I want to say his name was Cerberus, haha. "Cave canem"—"beware of dog"

Every day, we'd start class by the teacher saying "Salvete, discipuli!" to which we'd reply "Salve, magistra!"

The fact that all these years later I still remember some things from it shows its effectiveness I suppose.

In any case, in years since, I've used Pimsleur (for other languages), which is a similar "get actual language input rather than learning a set of language rules up front" method, and I like to think it's worked decently for me at least!