The amp is for better sound at high volume, or high volume at all with high impedance headphones.
A good dac will also give better quality with high quality headphones/speakers. I think it is the subtle background layers that become easier to percive, and less gritty sound aka better (clearer) highs.
How good the sound will be with your laptop depends on how good the sound chip and amp in the laptop are…can be shitty with no bass and grit as highs, but can also be okay to work with.
I use a macbook pro 2015. Not sure if that’s considered good/bad.
I took my ATH-M50x on a trip for use with a Surface Pro 4 and was happy with the sound. I didn’t do any rigorous testing, but they were loud enough and sounded good.
I have used Sennheiser HD-558 with jack to mini-jack adapter on a macbook pro 2013, was working just fine… now i have a focusrite audio interface and not sure if I hear any difference.
Surprised nobody’s mentioned the Sony MDR-7506 on this thread. They’re a studio standard for headphone monitoring and they’re about 80 bucks new. I got a pair a year or two ago and love pretty much everything about them.
AKG 271 MK2. A couple of years a go I tested most of the ones mentioned already, and they all sounded…good…lot’s of bass…great for listening to music, but maybe suboptimal for mixing. The AKG were the only ones that did not over-represent the low end.
I have these also. When I first heard them I thought it’s broken.
I think first and foremost you need headphones that sounds good else you won’t enjoy making music… over time you’ll probably learn how they coloring your sound by listening to your music everywhere and then can make a decent mix with them… at least that’s what I am doing 
Thanks everyone! A lot of good advice and headphones to research further.
These are surprisingly good: https://www.thomann.de/gb/superlux_hd662_f.htm?ref=intl&shp=eyJjb3VudHJ5IjoiZGUiLCJjdXJyZW5jeSI6IjIiLCJsYW5ndWFnZSI6ImRlIn0%3D <-- the “F” stands for flat bass response i seem to recall reading on head-fi.org. Or get the BOOMY one: https://www.thomann.de/gb/superlux_hd662.htm?ref=intl&shp=eyJjb3VudHJ5IjoiZ2IiLCJjdXJyZW5jeSI6IjQiLCJsYW5ndWFnZSI6ImVuIn0%3D
I will never buy beyerdynamic again.
OK, I’ll bite. There’s a story here begging to be shared. Why?
If you go Bluetooth, you should try Sennheiser HD4.40. (They work with a cable, too). I love those things. 90€.
“Beyerdynamic killed my father.”
-him, probably
I bought Beyerdynamic DT880 pro with 250ohms, after a lot of marketing hype. Including that Ohms nonsense. In fact the headphones can nicely reproduce transients, but it not linear at all. The bass is extremely thin and its kind of faded-in curve very impractical, and it has resonances on highs. The eq curve of it is so crappy that I never use it at all. Even my 25€ superlux hd681 sounds more helpful. Then the dt880’s clamp is made of metal and so strong that the headphones will hurt very soon on your ears. The marketing btw. praised it as a very linear headphones.
I have the same cans, and I do agree that they’re very thin in their bass response. I wouldn’t say there are resonances higher up, but it does almost hurt to listen to material with a lot of high end—it’s like anything above 10k feels like razor blades inside of my ears . It’s really weird…
That being said though, they probably have the best separation of any other headphone I’ve tried. You can almost see each sound. Even with the reduced bass response, if there are four kicks going on, you can hear every one of them as if they are completely separate objects. It’s like the difference between looking at a picture of a bowl full of fruit and actually having one in front of you.
I can’t say they’re pleasant to listen to, but if you want clinical imaging and reproduction, I’m not sure I’ve heard a better set of headphones. They make mixing issues pretty obvious. Just tweak the bass on another set of cans when you’re done! 
I also have the 880 pro…
Usually for tracking/mixing I use them with EQ, 4.8 db boost at around 35hz, then smooth curve up to the mids. Then you will hear the bass and the mids, good sub bass also although a bit blurry.
The normal response curve sounds good only with mastered music. If the bass/sub is mastered right, it will be present just at the point where you hear it clearly, but a bit less and you will notice it is too little by not hearing it clearly any more.
The really good thing with these is the stereo image is very wide and clear and outside the head. This also means the highs are boosted. When I had them new, they were a bit sharp but that settled.
Yes, Audio Technica ATH-M50 X are pretty good. That’s also my choice. I don’t have any active monitors, all the basics in mixing and mastering can be done with these headphones. And the price of 128 Euros is pretty low, too. By the way, these headphones were recommended to me by a professional, and I can recommend it to anybody else who’s interested in creating music.
My ATH-M50X arrived last week along with a behringer u-phoria umc 404hd sound card.
I was a little worried about running the card under linux but unnecessarily, just plugged in 
Both play great.
I can only recommend.
Senheiser HD600. More precises than HD650.
They are ugly but they are so flat, not boomy, goes down to 35Hz and spacious like some of “airy” AKG K6xx.