In addition to not being a professional music reviewer, I am also not a professional headphone reviewer. That said, I listen to a lot of music, and I listen to much of it via headphones. For most people, the value of headphones is a multiplier: the amount spent on headphones is worth several times what you'd spend on loudspeakers (in some cases as much as 10x); the same is true for the amount spent to amplify them (top end headphone amps can be had for under $300, but having it done it myself its easy to spend $1000 to mono-block amplify a $2000 pair of speakers).
My recommendation for headphones this year is the Monoprice Monolith m1060 v2 (affiliate link). Their MSRP is $299.
Most loudspeakers and headphones use what's called a "dynamic driver" (that's the cone-style circular speaker); most people have only ever owned dynamic driver speakers or headphones. The Monoliths are different: they use magnetic planar drivers: a thin rectangle of metal is suspended between two magnet arrays. There's a great intro article about headphone drivers at headphonesty.com if you want to learn more.
What makes these headphones worth recommending is that they punch well above their weight class. In my opinion (and the opinion of many reviewers), you'll need to spend more than $1000 to get something that sounds as good as this, much less something that sounds better. As you probably know, my tastes span just about everything: from metal to pop to rap to jazz and classical, and everything in between. These headphones are excellent at pretty much everything I've thrown at them, and they're extremely comfortable as-is (no need to change out pads or straps). The pads are made with (non-animal) protein leather with non-memory foam. I've used them for several hours straight with no sound fatigue and no comfort issues. The cable is removable, and with separate connectors for left and right it gives you the opportunity to get a balanced XLR cable, if that's your thing.
Why might you not want them? There are a couple reasons. First, the bass is very tight and present, but it isn't thumping. If you favor heavy bass response, these aren't for you. Myself, even though I love to listen to a lot of pop music (especially electronic) with lots of bass, you will hear the bass in these headphones, but you won't feel it inside your skull. The other reason you might not want these is that they are a fully open design, which means that sound leaks out of these headphones. This design is critical in allowing maximum air to flow (think of port holes in loudspeakers). This means anybody who is sitting near you will know exactly what you're listening to. These are not headphones for the office (or the bus), unless you have very understanding co-workers (or don't give a rip what your fellow transit riders think).
A quick aside about reviews: these headphones are on their second iteration. There were some significant issues with v1, including cracking wood, poor cable ends, and a head strap that could become detached. All these issues have been addressed in v2, so some reviews of the v1 will call out these things which are not an issue any more. Also, be aware if you good looking for a used pair to know whether you're getting v1 or v2.
If you pick up a pair of these, let me know what you think!
Want to be a headphone modder? This one's simple: you should try removing the foam that's sitting between the outer panel and the driver. It's a simple operation: remove the four PH00 philips head screws attaching the plate onto the wood, then gently remove the foam (it might be slightly stuck to the wood, so use a little force as needed), then replace the plate. Doing both sides will take just a couple minutes. Once they're out, you can test the difference by holding them to the outside of the plates (using your fingers to hold it around the outside edge of the foam, so your hands aren't blocking air flow). For me, this made the high end sound slightly clearer and more detailed. If you plan on using these outside where they might be exposed to rain, you probably shouldn't do this mod, since it exposes the driver directly to the air where it would easy to become wet.
The m1060s are moderately efficient (96dB at 1mW, with 50ohm impedance), which is to say that I could drive them with my laptop and my Google Pixel, though I was usually near the top of the volume when doing so. An external amp is not a bad idea, but not required. Neither of the alternate recommendations should need an amp.
If you're in the market for a stand-alone amp on the cheap, the FiiO A3 offers great portable performance for about $60. Its desktop brother FiiO E10K adds a 96kHz/24-bit DAC, switchable low/high gain mode, and a bass boost for only $75.
To step up a bit, I'd suggest something like the Aune X7s (class A) or Emotiva A-100 (class A/B). For a combination DAC/headphone amp, then my recommendation would be the excellent Aune X1s, which includes 384kHz/32-bit and DSD/128 support, and plenty of power for the m1060s (albeit not quite as clean as X7s's class A amps).