Another to consider is the Superlux HD681 EVO.
Out of the box they have a slow bass & upper bass boost (shocked me with how much bass they had, i really did not like it.)
But I have modded them, which has improved them significantly. (I seriously need get around to making a quick thread on my mod. Will edit in link eventually.)
After the Mod, the Bass is Tamed. Though leaves a little more Sub-Bass then what I am used to. A LITTLE bright, though it has NEVER been harsh, or too much for me.
Lastly, I HIGHLY recommend a High Power AMP that has absolute Minimal Coloring. For Example FiiO's E12. It is what I have, and Love it. Its a Straight Wire in terms of how it effects sound. Comes with Gain levels of "0" and "+16" And a Bass Boost. (I like their bass boost, it's subtle but makes a huge difference.)
The FiiO E12 and the HD681 EVO together may be squeezing your budget tightly, but I highly recommend. Or just get a cheaper Amp :/ The FiiO E11, A huge step down but looks like it'll do just fine. Or if you really wanna Cheap out, for for the E6 from FiiO, much cheaper, but will color the sound. (as you can tell I like FiiO's Amps when it comes to Portable)
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NEXT CONTENDER!!!
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Uhh, right... Well the SkullCandy Crushers may not be quite "Hi-Fi" as many other headphones. But they got built in AMP. (Convenient) And It has a Bass Control slider, aka "Get Its B-Ass where you want it to Shake." Not to mention... "Yeeea Maaaan! I got the Hip Schiit here man! ~They see me rollin...~"
Oh Kay, enough of my impersonations of the people I gotta Deal with. And my little reference. But seriously a headphone worth looking into.
It Has the Amp Built in, so no inline big bulky monstrous Amps some people carry... And a Decent but "Fun" Sound.
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The Next thing you should look into getting is some HQ Music Player after your First Basic Rig / Set up. HiFi-Man has a great low end Media player. only $120 (make sure your looking at the standalone, not the ones paired with their higher end Ear Buds.) Obviously It's going to be a while before you start getting ready for another purchase, but It's what I'd recommend you do next.