What does "cheap Sony CD player" mean?
I am a firm believer in component matching and trying to obtain synergy. Headphones only give out as good as what is going in. The source is just as important, if not more so. If you are spending money then I am one for proportionate spending across your whole audio chain (except for cables which should come dead last and when you have exhausted everything else

)
Your Sony separate may well be *decent*, as old does not necessarily mean it is not good.
I wouldn't worry about the technical side. My ESW9 do not technically need an amp,
but are they improved by one? Hell my Sennheiser PX100 are improved by amping - which only serves to underline how much of a bargain they are. I firmly believe the PX100 is a headphone everybody should own. Budget goodness
For the time being I would spend time listening through the headphone output on the Sony to become accustomed to it. Then listen through the amp and see if you hear any differences. Don't bother with the speaker comparison