What headphone and amplifier for classical enthusiast

Hi RV it's Jim here, you may know that I only listen  to phones nowadays and totally love the experience. You can wake at 3am on a sleepless night and take yourself to heaven without waking anyone. The phones I have are Sennheiser HD 800 and they are supremely detailled and tonally correct (once fully run in). Headphone amps are a different matter of which I use the Luxman P 750u which is unfortunately very expensive but of all the head amps i Have listened and that is a lot it has consistently blown away all the others. The head amp is solid state but with a slight touch of warmth, all I have done is connect my PS audio DSD Dac and aural magic for hours on end. At the moment I am listening to Beatrice Rana's new Chopin recording and very fine it is (she is turning out to be very special indeed.). I hope you have luck in your quest. Jim204

@OP

I do not know if this is important to you , but the Pro iCan  comes with a remote,  but a simple one.

Thanks to all of you for your help.
I have to digest it all.

I’m a real novice in this field. I’m embarrassed to ask a very basic question. Besides the headphones and headphone amplifier, how do I connect with my sources (Cambridge streamer, Cyrus CD transport, Oppo player?)
With my speaker system I have a modified Conrad-Johnson PV 11 preamp, Benchmark DAT and amplifier.
Sorry to be so uninformed.

streamer / CD Player -> preamp (line out, an unused one) -> headphone amp -> headphones

I would guess your output 2 on the back of your Connie J is available to plug in the head amp.