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).
Music keeps me energized all day (and into the night) at work — 70% electronica/dance/DNB, 20% rock, 5% hip hip and 5% other/classical — but I’m tired of low-quality sound and I’m ready to put my money where my ears are. I want to buy a USB DAC + Headphone amp, buy headphones (or, per your recommendation, to buy 2 pair) to complement the amp and my choice of music, and get great desktop sound for around $350.
Cable dressing and length: Most stereo headphones have just one cable, usually attached to the left earpiece (sometimes called single-sided cabling). Some models -- and all earbuds -- use a Y-cable that connects to both earpieces (double-sided). The actual cable plug, meanwhile, is usually one of two designs: a straight I-plug or an angled L-plug; the latter may be useful if your portable player has a side- or bottom-mounted headphone jack.
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.