I’d second the Shure 1540. It is an incredibly musical headphone that I’ve had for several years, listening to jazz, rock, pop, electronica, funk, and rap. It has good tonal balance (though not super-neutral per se), and reaches deep when needed. It’s not too hard to drive, but responds well to power. I’ve used an Oppo HA-2 SE, a Burson HA-160, and an SPL Auditor with it. I’ve been very pleasantly surprised by how well it works with all of them, as well as different DAC sound signatures (the Oppo vs. a Gungnir MB in my living room). It can be found at prices well within your budget, and open-box or used units for less.
It’s also light and incredibly comfortable, with Alcantara ear pads (and a spare pair included!). It scales well with better aftermarket cables- I am using a Moon Audio Blue Dragon to good effect.
As you can tell, I’m a big fan- it’s my daily driver.
The only three things that are negative and worth noting: 1) The headband may wear down and flake after a couple of years, but you can add a headband protector to help this. 2) It is not the last word in detail- but that also allows you to listen to older recordings without notable fatigue. 3) It isolates well, but not great. You can wear it and listen to lower volumes with a person nearby and not bother them. However, it won’t help too much with significant ambient noise. Great for a quieter office environment, but not a loud one.
Highly recommended, and good luck with your search!