As a person who records music, and uses phones for monitoring mixes, I think earbuds are inferior to headphones. As before mentioned buds damage more easily, and have poor low ends. The driver style buds are better than standard ones (I have a pair cost about $90).
For complete silence for people near you (in a Library or near angry Dads) closed headphones are the best! They have less dynamics than open headphones.... for example the Sennheiser HD480 will give near naught out (that is to others near you) and are good for you to hear your music if you're in a noisy place (like a train station..) These cost about $200-$300 pair.
As far as anything below $60 goes, go to your nearest hi-fi store or like, and get ones that the padded part presses on your head, not the ear. That's the closest you'll get for sound quality and also not disrupting others.
Alternatively. use ANY type of head/earphone you like, just TURN IT DOWN (like your dad is probably nagging you to do). It's best for your hearing and not bothering others. If you're wearing any kind of earphone and others can distinguish the music you're listening to from a few metres away, then you're probably damaging your hearing.
Yes, if you're in a loud environment, you'll turn headphones up louder to drown out background noise, thus risking damage. Earbuds are good to block out background noise, but deliver the sound much closer and more directly to the eardrum, therefore take not much turning up to be damaging.
BTW I have hearing damage due to firecrackers when a kid, and trust me, No music is cool enough to make it worth damaging your ears by turning it up too much. 24/7 ringing in the ears is nasty.