This would be a difficult topic to know how to search for here.
I recommend you search for [headphone amp] or [cafe walter].
You will get all the threads that discuss this topic.
Here is one thread:
Best sounding headphone amp?
I use Transcribe! software on my computer to play mp3 and wav files, into a Fodera Practice Amp. I don't think they make it anymore, but the Cafe Walter is similar and from what I read just as good. One of the great things about these is that you hear more string and fingering noise that you normally would through the speakers of an amp, so it...what would the word be...it encourages you to work on playing cleaner.
The Transcribe! software allows me to loop a specific portion of a song, slow it down, and filter out the guitars and vocals, to concentrate on learning the bass part.
There are small practice amps that have a mini audio jack in and a headphone jack out, that can be used for doing this also.