Along with the wire the metal used for the headphone jack is also essential. Most bundled headphones have a nickel plated plug, which is not a preferred option. A Gold Plated jack works really well with a copper clad aluminium wire in increasing conductivity and is the second most common metal used. The best however is one which has a Silver plating
The two most common headphone plug sizes are 6.3mm (1/4in.) and 3.5mm (1/8in.), (3.5mm being the most common jack size as of now for mobiles, music players, tablets and laptops.) Adapters are sold to flip the two either way and are also bundled along with a few high end headphones.
As for a few old mobile handsets that use a standard 2.5mm plug, earphones are especially available for those. It is normally mentioned on the device you are using, please check that before you choose the headset for your device.
A L-shaped Plug is mostly preferred over a straight I-shaped plug. The main difference is: a straight plug would be more suited for when the cable would be coming out straight from the audio playing device, For eg: right from the mp3 player in your shirt pocket. Where as the main advantage of the L shape plug is that it has less chances of you snapping or bending it, causing any kind of damage while your phone or mp3 player is in the pocket.
How this works is, with any kind of movement, the L-shaped plug also swivels around, not causing any bends in the wire. The straight plug doesn't do so causing the wire to get entangled or tug upon something.