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Yep, either a hifi amp for both speakers and headphones or some easy option of sound out from the main amp to a headphone amp if that will give a noticeable sound improvement.
In terms of headphones budget, probably £300 or so. Wired, over ear, not fussed by open or closed. Listen to most stuff but not much in the way of electronic/dance music.
In terms of amp(s) I'd guess up to about £500. I haven't started looking at all yet, just trying to understand what I need and what I should be looking for.
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I just picked up these Meze 99 classics for £269 - love them. Mainly listening through a Chord Mojo DAC/headphone amp which I also use as the main source for my amp.
Think this 'non-review' of the meze does a good job of explaining why I like them https://youtu.be/M4_KkRewxBg
Source>DAC and/or headphone amp>Headphones.
What's your budget? Open headphones? Closed headphones? Over ear? On ear? In ear? What do you listen to etc
Edit: Sorry, misunderstood. You want to use a HiFi amplifier for both speakers and headphones? Some of them have okay headphone outs but really it just depends on the type of headphones you're gonna buy.