for under $100 i would say get the Grado SR80's, great set of cans to start off with, however, upon hearing Grado's you're going to instantly want to upgrade to a higher model. SR80's probably won't give the bass that you are looking for though.
Some people have mentioned A500's, haven't heard them but the A900's are very nice, as a closed set of cans the bass is fairly decent as well.
Seems one of your priorities is construction/build, from what many people have said about the HD280's, the headband seems to be flimsy.