Looking for closed back headphone advice

Most headphone amps are afterthoughts, so generalizing that a dedicated headphone amp is normally going to be better than one included in a receiver, integrated, or preamp is anything but "puffery".  My Modwright LS 100 has a pretty decent headphone amp, but that's an exception, not the general rule.

With a highly efficient set of inexpensive headphones the difference may not be very noticeable, but I guarantee you that listening to a high quality source with a high quality set of hard to drive headphones like LCD-4 will be a completely different experience with a quality high power headphone amp than with the headphone amp in most integrated amps.

Bel Canto C5i is another integrated amp (digital) that is also a very good headphone amp. 

There are exceptions to every rule, but in general dedicated headphone amps are superior to headphone jacks on integrated amplifiers. Also, CD sound can be further improved by the addition of a quality DAC which often includes headphone output with a volume control. You won’t believe it until you try it.

If you can pick up a pair of the Oppo PM-3s at a good price, they are very, very good and you can drive them with an I-phone with good results.  They were $399 new and are no longer made, so some people are asking high prices, but check around.  Also, the PM1 and PM2 are great as well, but more expensive.  The PM3s are really great though and fit your criteria very well. 

I want to recommend you Sony MDR-Z1R , cos i bought them and i like them