i don’t imagine I would need quite as powerful or expensive a sub as those who mainly listen to other types of music [than classical], but I may be wrong.
Indeed, I believe this rests on a misconception, albeit an understandable one; power and "exactitude" is an important basis for finesse and insight, I find, as is displacement area to cover the whole envelope and (all things being equal) make for lower distortion (i.e.: smaller cone movement for similar SPL). Sensitivity (again, all things being equal) would also be of importance, though very high sensitivity subs are harder to come by and physically incorporate, given these would likely take up a lot of space as horn loaded designs or ported dittos - insofar they're even tuned for commercial use (cinema subs here would be the better option here, rather than typical PA subs).
As commercial subs goes there seems to be consensus on sealed designs being easier to integrate with the mains, but I imagine (actually know for a fact) that properly integrated ported subs can make for an excellent extension of the main speakers, though I would add they generally sound different than sealed subs. To my mind a sealed sub generally excels over a ported ditto in being "more quiet" when not called for, or perhaps this is a way of saying that in any kind of sonic action it leaves a slightly smaller, or smoother fingerprint. To some this may translate into something missing, perhaps not least while watching films, but to others it may be just the thing, not least with music, to make it all mesh better.
From a more pragmatic point of view (even with the proviso I don’t know your main speakers) my advice would be to go with a sealed, powerful sub preferably fitted with a 15" or upwards, very powerful and larger voice coil diameter driver, and with extensive DSP capabilities for proper integration. In my own setup I use the SVS SB16-Ultra with great results (incl. the outcome with classical music) - indeed a sonic beast in the best sense of the word, in service of both insight, integration and sheer brute, effortless force when needed. Though I’ve never heard it the Funk Audio 18.0C also seems like a great choice.