I want to thank both
lhorwinkle and
Ted for your feedback. I've taken it all in.
Well, when I started this question, I was getting confused by discussion on another site, because people seemed to be discussing headphones based on the listening pleasure they were getting. some of the headphones had a "fantastic bass", "amazing treble" and so forth. I wasn't sure what that meant, because I didn't understand the technology enough. Put simply, if I am trying to learn to bring out a soprano line, making it louder than the lower pitched accompaniment, I don't want anything boosting it artificially, or I want be able to tell what I'm actually doing as a learning pianist. I didn't know whether that is what these "amazing" things were doing. I wanted what I'm doing to be reflected in what I'm hearing. At this point, I'm rather sure that what I was imagining isn't what was meant. (I've done some studying). I.e., whatever the "amazing" headphones do does not involve artificially changing the produced sound in my ear.
I did discover something, though, when I plugged the little ear buds into the piano via the adapter, and then went back to my Sony headphone. As I related, I played the same passage twice, making sure I was making the same physical movements, and the ear buds did not catch the dynamic contrast nearly as finely, so that there was a disconnect between what I was doing and what I was hearing. That would be detrimental to learning to play. So I know that quality of ear phones (or particular qualities of ear phones) can have an effect on our learning to play. At least I got that far.
BTW, if you intend to plug the phones into your piano, you'll need to buy low- or moderate-impedance phones. The high-impedance phones will usually require a headphone amp. That's another $100 load on the wallet.
In the under $300 range most phones range from 32 ohms to something under 100 ohms (or are available in multiple impedances, one of which will be in the low range), and these will work with the piano.
You start running into trouble with phones that are at 300 ohms or more. But most of those are in the high-price range, far more than I'd ever spend.
A couple of weeks ago I wouldn't have understood anything other than that the more expensive ones aren't worth it, and you need a secondary thing, the amp. I was running into so many words like ohms and impedance (never had high school physics; went to school in the 1960's when technology was way different) - a Coursera course on technology came along and I'm in the middle of it.

A bit of overkill, but at least the lingo is starting to make sense.
Closed phones are sometimes too bassy, and they're frequently head-clamp painful.
I even understand why they're bassy, now

- feedback on various closed 'phones often mentions the head-clamp problem.
But you seem to be favoring closed phones to help keep background noise OUT.
I have tried to record things for my teacher, and in the middle of it, somebody goes to the microwave and you hear arhythmic "beep beepbeep ...... beep beepbeepbeep ... beep-beep-beep-BEE-EE-EE-EEP" (I'm recalling a recent session where that happened repeatedly and that's my motivator. i'll have to ask myself how often that actually happens.)
I've also been tempted by the new Sennheiser 579 open phones at $120 (recently on sale for $100 at Amazon)
The one I kept hearing about was the 598. Now I'm looking at the 579. Do you know how it might be different? (Of course I'll be looking that up next.)
I'm looking at Canadian prices. It says it was CAD $269 and has been reduced to $139 (CAD).
Currently I use Sennheiser HD 6XX (closed)...
That's the one folks were gravitating toward on the other site as superior to the 579, but it was something like more than twice the price.
but I still often use my Grado (over ear), particularly for piano music, as they have a wonderful clarity nothing else has matched so far...
I have not heard of this one before. Interesting. Clarity is good, I'm thinking.
As with sound equipment in general, above a certain quality the effect becomes very subjective.
That makes sense.