i really think you'd do much better if you bought good headphones, then a separate mic.
the ones that are typically paired together under $100 won't be very good for music. even for computer gaming they're kind of mediocre. and i think if you go seperately, you'll actually probably get a better mic and better headphones for your money.
so really, i think the question is what decent pair of portable headphones can you get for $20-$80, and then maybe what portable $20 mic is going to do what you need it to do?
you don't want to be walking around listening to your MD with a boom mic on your headset anyway, not only would it look weird but i think it would get really old, fast, and you'll be stuck with something that doesn't work very well for just music, and doesn't work very well for your intended recording use either. usually boom mics are designed to record what is directly said into them, not pic up speech elsewhere. so for recording a lecture, it's not going to work well unless you get the prof to actually wear the thing, lol.
in terms of portable headphones, i think the sennheiser px-100 are a great place to start. note they're open canned. they'll sound better than closed cans for the price, but the design has other compromises. search the forums for info on px-100. others will chime in with other recommendations for you to check out, and probably ask you some more questions. but i think the px-100 is a great portable headphone, at least for my uses which don't require listening in noisy environments.
