As far as choice:
Get them Audio Technicia m50x joints for the crib or studio and them bodega bum 10 dollar Bubble Gum 2 headphones from iluv for the phone/ipod/gym and you'll be good and not care if it breaks. If you want one with a mic and better quality for the phone, then get the skull candy joints which are pretty durable but the quality can vary depending on the model.
I owned three Audio Technicha joints and they have a warranty for their products or at least used to do that. I had the Audio Technicha m50, got a replacement and then bought the m50x from amazon. How I broke my first pair was due to me falling asleep in them too much and rolling with them on my head, the second one broke because I kept dropping them due to me taking advantage of the long card and walking around with them for far distances in my house. I mean the chord was so long I would forget that it was there till it hooked on to something and my head phones fell lmao.
However with these m50x joints I have now though, they have good sound quality, a replaceable cable so if it breaks you can just by another one. The only downside to them is that the chord is shorter than the super long Audio Technicha m50's but they lasted me over a year so far and still work very well. With this said I recommend Audio Technicha. The ones I had that broke were because I was a dikkhead and any headphone would break it if you drop it one million times and abuse it.
As far as care:
Don't sleep in them lol
You may not want to wrap the chord all around them like some people do because that may stress the chord and the ear cups. So if you do that don't do it too tight.
Don't drop them
And with cheaper headphones you get what you pay for so you are taking more of a gamble anyway
These are the only steps I have. The truth is all headphones conk out eventually and it's only a question of when. Take it from me, a guy who owned many throughout the years. You could treat them like a baby and they will still mess up on you one day.