I think it’s fair to compare the Grados and HD598, but the M50 is very different and seems not to fit in that comparison. The DT770 is a better comparison to the M50, although the 770 is a better more expensive item. A long time ago I had a Grado 325 and a Sennheiser HD565 – very similar, very enjoyable. Today for that type of sound I might choose the Soundmagic HP100.
I’m looking for a pair of studio headphones but I can’t decide. I want to produce dance music on these headphones since I don’t have $$ for monitors. The three headphones that I read most positive reviews about are the Shure srh 840, GMP 8.35d and the KRK KNS-8400. I read the GMP 8.35d are the best but I can’t test them since no shop sells them in my area.

Total harmonic distortion: True, headphones with lower actual total harmonic distortion (THD) will sound better than those with higher THD. But the quoted THD numbers -- "less than 1 percent" -- aren't helpful in predicting sound quality. Listen to recordings of simply recorded acoustic guitar to assess the distortion of one set of headphones versus another. Some will sound appreciably cleaner than others.

I see, yes, but that should serve as an important lesson – the soundstage is not real in the same sense as actual tones, bass, treble, whatever. Soundstage is a perception that’s based on many factors, and here’s a challenge for you: You should be able to find some music tracks that have better soundstage on one headphone, and other tracks that will be better on the other headphone. Most of the time it will be just one way, but when a closed headphone beats an open headphone, I expect the open headphone will still show an advantage on some tracks. Your hearing perception could be tricked by simple things like a recess or emphasis in certain frequency ranges, or even phase shift when more than one driver is in the cup.

Portability can mean many things, such as appearance in public, having a secure fit so the headphone doesn’t shift off of your ears, amount of isolation from ambient noise (including active noise canceling), whether the headphone can be worn around the neck when not listening or it requires a carry case, and when extra amplification is required, whether a suitable amp can be found that’s OK to carry along with the portable music player.

There are many good articles here on Headfonia. You could click on Buyers’ Guides and read through those, then click on the Headphones topic header for each individual report. The “process” you go through is learning your own sound preferences, then matching that to the products that are available. It is a process, so you have to learn the major differences. Any shortcuts you take might be OK, but when you buy something that you discover you don’t like, make sure you can return that item.
The QuietComfort 30s are Bose’s wireless in-ear headphones with active noise cancellation, and they’ve set the bar for the category since they were released in 2016. The QuietComfort 30s utilize the same StayHear+ tips as all Bose’s other in-ear headphones and they use the same app as the company’s other QuietComfort headphones. The one caveat is that the QuietComfort 30s are a neckband-style of wireless headphone, so they’re fairly heavy and probably best served for office settings.
Circumaural headphones (sometimes called full size headphones or over-ear headphones) have circular or ellipsoid earpads that encompass the ears. Because these headphones completely surround the ear, circumaural headphones can be designed to fully seal against the head to attenuate external noise. Because of their size, circumaural headphones can be heavy and there are some sets that weigh over 500 grams (1 lb). Ergonomic headband and earpad design is required to reduce discomfort resulting from weight. These are commonly used by drummers in recording.

The iPhone will drive the headphone fine and make a very nice sound, but the amp will make a big improvement in harmonic extension and soundstage. Use the amp whenever possible. Both Headfonia and I concur that the E07k is a great amp, and probably the best thing you can get for up to twice the price. I’m familiar only with the E07k, the E17, and the E12. I think the E07k beats the E17 (and both are also USB DACs), while the E12 is just an amp, and has a darker sound but with more power for inefficient headphones. The Philips is not inefficient.
I’ve had only a few minutes one day with a 598, so I can’t say exactly. But since the HP100 is closed and the 598 is open, I would get the 598, as long as open back is OK for you. I don’t think you can go wrong with the 598 in any case – it’s a very good headphone. Watch carefully for any cracks to develop though, since there were many reports of that.

Released in 2017, the Bose SoundWear Companion is a different kind of wireless headset. It doesn’t have any earcups or earbuds, but instead it sits around your neck adn has speakers that shoot sound up towards your ear — it’s essentially a portable speaker that sits around your neck. It’s water-resistant, so you can technically work out while wearing it, but it’s really designed for the person who works at home. It’s comfortable enough to wear for lengthy periods of time, but it also has excellent built-in microphones and works great as a speakerphone.

Unlike with other codecs, AAC test signals from Android phones like the Huawei P20 Pro, LG V30, and Samsung Galaxy Note 8 all vary wildly. Though we can’t definitively say why each Android device seems to handle AAC encoding differently, the fact of the matter is that only Apple can do it well. We suspect some of the power saving features baked into the Google ecosystem’s varying hardware has consequences for audio playback. Nowhere is this more apparent than Huawei’s power-sipping P20 Pro, which seems to cut out at around 14.25kHz.

If you’ll mostly be using headphones at your desk, install a headphone hook so you can safely stow yours when you’re not using them. Headphones can be fairly fragile, so it’s important to take care of yours and avoid tossing them around. A headphone hook gives your favorite pair a place to hang and creates a fun conversation piece for your workstation.
Earbuds have small speakers that rest on the ear canal of the wearer. These are usually much less expensive than on-ear and over-ear headphones and reproduce the sound well. However, outside sounds, such as traffic or power tools, can get past the earbuds and interfere with your enjoyment. Earbuds also don't stay in place very well if the wearer is moving much, such as exercising. These also are lower fidelity than on-ear and over-ear headphones.