Looking to upgrade my setup from iPod Touch 6th gen and AT-M50s

[RikuAotsuki]

I was hoping to NOT need to ask for recommendations, but after looking around, I'm suddenly unsure of how well what I was going for suits me, so here goes.
 
Currently, I have an iPod Touch 6th generation, and listen with AT-M50s. I had initially intended to purchase a FiiO X3-II, but after a bit of reading I discovered that it probably wouldn't be the sound upgrade I was looking for. My iPod has a shattered screen, and isn't really charging properly anymore, so I intend on getting a new player regardless. I've heard the clip+ has fairly good sound, and the expandable memory is certainly a plus, So I was thinking of getting that instead and upgrading my headphones for a more significant sound quality boost. Of course, if there's a player significantly better(I'm new to the technical aspect of this stuff, so even after reading up on it, I can't really specify how) and of a price similar to or lower than the FiiO, I'd be willing to get that, and better headphones later on, as I had already intended to.
 
As for headphones, I do really love my M50s, but I know they're entry-level. They're uncomfortable after a couple hours of wear, and get a little too hot around my ears, but I've been overall pretty happy with them. Still, I want to upgrade. I listen to a fairly wide range of music, so it would be inadvisable for me to get something overly tuned for a particular genre, but a lot of my favorite music is heavy on the lower tones. Even then, though, I don't want something that sacrifices higher tones to do so. My budget, between player and headphones, will max at 600$, though there's some wiggle room if recommendations involve an amp as well. I tend to listen at home, or on walks, so I don't mind sound leaking, but I'd like a degree of isolation from outside noise. I'm pretty flexible on those details. I'll list some of my favorite songs, so you guys can get a better feel for the type of sounds that're important to me, since I know my ability to describe it is limited at this point.
 
Moonspell- Abysmo
Moonspell- An Erotic Alchemy
Moonspell- Medusalem
Dead Can Dance- Opium
SID- Monochrome Kiss
Assemblage 23- Let Me Be Your Armor
Symphony X- When All is Lost
Dimrain 47- Twilight Techno
Furries In A Blender- Don't Hold Back
Love Spirals Downwards- Illusory Me
 
I apologize if this isn't enough info; I'm more than happy to elaborate if I missed anything. It's also 4AM right now, and I spent the last three hours trying to make this coherent. Thank you in advance for putting up with me.

 

[serman005]

  I was hoping to NOT need to ask for recommendations, but after looking around, I'm suddenly unsure of how well what I was going for suits me, so here goes.
 
Currently, I have an iPod Touch 6th generation, and listen with AT-M50s. I had initially intended to purchase a FiiO X3-II, but after a bit of reading I discovered that it probably wouldn't be the sound upgrade I was looking for. My iPod has a shattered screen, and isn't really charging properly anymore, so I intend on getting a new player regardless. I've heard the clip+ has fairly good sound, and the expandable memory is certainly a plus, So I was thinking of getting that instead and upgrading my headphones for a more significant sound quality boost. Of course, if there's a player significantly better(I'm new to the technical aspect of this stuff, so even after reading up on it, I can't really specify how) and of a price similar to or lower than the FiiO, I'd be willing to get that, and better headphones later on, as I had already intended to.
 
As for headphones, I do really love my M50s, but I know they're entry-level. They're uncomfortable after a couple hours of wear, and get a little too hot around my ears, but I've been overall pretty happy with them. Still, I want to upgrade. I listen to a fairly wide range of music, so it would be inadvisable for me to get something overly tuned for a particular genre, but a lot of my favorite music is heavy on the lower tones. Even then, though, I don't want something that sacrifices higher tones to do so. My budget, between player and headphones, will max at 600$, though there's some wiggle room if recommendations involve an amp as well. I tend to listen at home, or on walks, so I don't mind sound leaking, but I'd like a degree of isolation from outside noise. I'm pretty flexible on those details. I'll list some of my favorite songs, so you guys can get a better feel for the type of sounds that're important to me, since I know my ability to describe it is limited at this point.
 
Moonspell- Abysmo
Moonspell- An Erotic Alchemy
Moonspell- Medusalem
Dead Can Dance- Opium
SID- Monochrome Kiss
Assemblage 23- Let Me Be Your Armor
Symphony X- When All is Lost
Dimrain 47- Twilight Techno
Furries In A Blender- Don't Hold Back
Love Spirals Downwards- Illusory Me
 
I apologize if this isn't enough info; I'm more than happy to elaborate if I missed anything. It's also 4AM right now, and I spent the last three hours trying to make this coherent. Thank you in advance for putting up with me.
 
 
These two are sort of inconsistent with one another. Either sound leaks significantly, or it does not. We can't have it both ways. There are some semi-open cans out there, but still, they do always leak. Put another way, good isolation is by definition related to non-leakage. Given all that, do you want open or closed cans?

 

[RikuAotsuki]

Ah, didn't really register that they were directly related. Closed is what I'm used to, so I'd guess that I'd prefer them on a familiarity level, but I've never listened with open cans before. I'd certainly be willing to give them a try if they're highly recommended.
 
Edit: I'm looking at the Beyerdynamic DT770 80ohm, would that fit what I'm looking for? And, given that the 770 and clip+ would put me decently under budget, is there an amp you guys'd recommend to go with, or would it be entirely unnecessary?