Headphones.
I first used some cheap ones and then switched to Bose. The difference was significant. Never again cheap headphones..
Also my ears thank me because I can listen to music with lower volume than with the cheap ones.
Sennheiser is a good choice for someone just getting into higher quality gear. They have a wider range than most, but even their lower end are very good.
I have a pair of relatively cheap yamaha studio monitor headphones that are actually pretty great! ($80) Most headphones will also sound much better when driven properly with an external DAC, especially the higher end ones.
I plan on going to the $200 range next as I'm not too satisfied with the bass of these things, It's definitely there, but it doesn't go too loud before it gets distorted on the lower ranges,
I decided that if I could keep a pair of cheapo ear buds for a year, I would get myself a nice pair. (This was about 3 years ago)
Last year I got myself the top of the line Sony ear buds. But they hurt my ears (not the newest ones that hurt people's ears, the year before model, c'mon Sony, what are you doing), and my cheapos still work wonderfully, so unless I'm in a noisy environment and I need the noise cancelling Sony provides, I just roll the cheap ones.
Over the ear are another story though, those you go good or go home.