K361-BT

Classic Sony MDR-7506, AKG K361 from your list. Wire usually has better sound than wireless (convenient and noise cancelling). I would not risk sweat on them for light running, the smell stay on earpad during your long study session.

1. Sennheiser Momentum 4 - Magical. Don't know how they pack in the sound quality there. Sometimes I trash the EQ settings just to try to make them sound bad. I baby them though, so my number 2 is 2. AKG K361 - Cheap, sounds great, and comfortable as heck to my head and ears. Never offensive, easy to drive, good durability. I'll carry and use these without a care while the M4s would stay in my work bag. When I'm at home, though, I generally use my number 3, the 3. Fiio FT1 - Does the same thing as number 2, just with a little more style, cost, and weight. I love the wood. Driving it through 4mm balanced on my Fosi K7 sounds sweet and rich. I got these to replace #4, the 4. Audio-Technica M50x - This was my go to for seven years before last year. Built like a tank, I went through a set of pads on it. For a long time this was what I thought headphones were supposed to sound like. I'm glad I mixed it up. Speaking of mixing, let's talk about number 5. 5. Sony MDR-7506 - I got these because I wanted to see what the fuss was about. I get it. If you can make your music sound great on these, you can make it sound great on anything.

From least to most favorite: Audio-Technica ATH-M50X - well-built, cohesive imaging, but some of the most unnatural-sounding headphones I've heard, having a huge hole in the lower mids, mud-fest in the bass, and harsh peaky treble Audio-Technica ATH-M60X - well-built, surprisingly spacious for how small they are, but still a hole in the lower mids and shouty ear gain, plus they're on-ear and therefore uncomfortable Audio-Technica ATH-M40X - well-built, decent all-rounder, but still lacks the lower mids and mid-bass is too boomy, plus the treble is a bit sibilant Sennheiser HD280 PRO - great isolation, large pads, cohesive imaging, but too much sub-bass giving me a headache, too dull yet grainy, plus the cable is microphonic, heavy, stiff, and non-detachable AKG K361 - the most tonally balanced overall, but not very impressive technically, having kind of a tinny timbre with metallic treble, mediocre imaging, and some of the worst build and comfort with a huge design flaw - earpads have a lot of compression with pressure affecting the FR, creating constant channel imbalance, so you have to be perfectly still while using them AKG K371 - the same but more natural timbre for the sacrifice of warmer and muddier tuning Sennheiser HD620S - nice build, comfort, and isolation, good clarity, but unpleasant, cold, harsh, focused, claustrophobic, fatiguing tuning with wonky low-end Adam H200 - nice build, comfort, and isolation, surprisingly spacious, good bass quality, but too shouty FiiO FT1 - the best all-rounder, most casual, most comfortable, solid tonal balance, spatial qualities, and bass quality, but too much bass and too peaky unrefined treble, making them sound fatiguing Beyerdynamic DT770 PRO 250Ω - the best clarity, sounding almost like an open-back, great all-rounder, great low-end and midrange, decent spatial qualities, decently comfortable, but too sibilant, making them unsuitable for a certain kind of music NOTE: I also had the 80 and 32Ω versions of the DT770 but didn't like them as much

I'd recommend stretching your budget for the AKG K361/371. 371 is more expensive than the 361 and has a more fun sound than the analytical 361. I found both to have great imaging and decent soundstage for a closed back. I don't know much about mics. I rock a 720p logi webcam and the mic works well enough.

Either my AKG K361 or KPH40. There are certainly “better sounding” things in my collection but none as versatile. Hifiman Edition XS build is dogshit and leaks sound like crazy, and IEMs irritate my ears if I start using them exclusively for multiple days at a time. If just sound specifically, my Softears Volume S would have no competition.

For entry level I have the AKg K361. Very balanced tuning. Things like imaging and soundstage are middling but it sounds good. ThebAKG K371 is a warmer variant and more popular. Fiio FT1. Is a warm/dark headphone with high level technical performance (imaging/detail retrieval at its price point). Tuning is more hit or miss depending on who you are. But still a good option. For a dac all these headphones are easy to drive and I would recommend a Fiio KA11 for $30. I think this would be a solid foundation to start your audiophile journey 

Creative Aurvana Live SE (not the 2) or E-MU Black Walnut. AKG K361 are workable for games, but not as good for them. Better comfort and isolation, though (unless you have small ears, maybe?).