The FiiO E17 “Alpin” + AIAIAI TMA-1 or Pro700 Mk2 seem like a mix you’d recommend, but I’m concerned those cans will be uncomfortable for day-long use.  Also I don’t know if that DAC/amp is the best for my style of music/headphones.  Third, some of my techno tracks have stunning vocals, and I don’t want to miss out on those high notes while enjoying the bass.
If you just want to block out sound without active noise cancellation, good over-ear headphones will naturally do that to some extent. This is called noise isolation, and it simply works from the earcups forming a good seal over your ears to prevent outside noise from getting in. It's not as effective, but it's less expensive than active noise cancellation and doesn't require power.
Interestingly, yesterday I was comparing my beyer 770 with my AT ath30 and then I realised how important it is also the soundstage, the good separation of instruments … finally I have decided I want to take this into account as well, and not only the issue of bass, midrange and treble … Since, in my opinion lack of bass we can try to fix it, but lack of soundstage is impossible, right?
Open back usually results in more natural sound, but they leak sound in and out. This means you probably can’t use them in a library or a plane flight since the sound of your music will leak out and disturb the people around you. You also can’t use them on loud public places since noise from the outside will disturb your music. Therefore, even though open back would give you more natural reproduction, for these reasons their use is limited to mostly at home or in the office (if you have your own space that is).

I tend to regard the M50 as the minimum for hi-fi listening with no apologies for limitations. But if you have to go cheaper than the usual $125 USD for the M50, the B&O Form2 with a simple bass boost gives a real hi-fi sound, and it should be available for about $100. The Beyer DTX-501P (similar to soundmagic P30) is good for $100, but needs a slight treble boost. The LSTN Fillmore with wood cups is somewhat colored, but still a good listen and good for $100. Below $100 are the Sennheiser PX series – not hi-fi by any means. There are several good IEMs below $100, and Apple Earpods with a Dirac or Accudio Pro player are very hi-fi, and cheap.

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.