You want a portable amp? If I were looking portable, I'd look at the Fostex HP-P1, which combines an excellent DAC that takes digital output from your iPhone/iPod. If you are looking at it for actual portable use, as in walking around town, you'd look pretty silly with a pair of Audeze or Stax on your head. Beyer DT1350's are pretty good, but I personally prefer IEM's to having cans on my head while moving around. You can drop anywhere from $300-1300 there for really good IEM's. Customs would be at the high end.
Now if you are talking about putting together a headphone rig with a dedicated amp that you are going to use at home, which I believe the previous poster is assuming, then I'd point you straight to Audeze. In your budget the LCD-2 rev. 2 can be had on the used market along with a suitable amp, of which there are many to choose from (I use a Violectric V181). There should be quite a few LCD-2's on the used market these days since the LCD-3 just came out at almost double the price. The latter is an excellent choice as well, but out of your budget, and will be on backorder for a while. Not a fan of HiFi Man's offerings, and the better of them (HE-6) have a much more limited choice of suitable amps as they require much more power to make sing. I'm not a fan of old Stax at all, but the newer stuff they've put out when amped well is excellent (007 and 009). All way over your price range though and you may even prefer Audeze, or at least wonder why people are willing to pay so much more for Stax.
As far as having "the same level of musicality"...well, OK, but don't expect them to be speakers. It is a different experience of enjoying music. It will never be speakers though. Then again, you may enjoy it even more, certainly some seem to. I'm not one of those, I much prefer speakers, but when privacy is necessary, the option is certainly nice to have available.
Now if you are talking about putting together a headphone rig with a dedicated amp that you are going to use at home, which I believe the previous poster is assuming, then I'd point you straight to Audeze. In your budget the LCD-2 rev. 2 can be had on the used market along with a suitable amp, of which there are many to choose from (I use a Violectric V181). There should be quite a few LCD-2's on the used market these days since the LCD-3 just came out at almost double the price. The latter is an excellent choice as well, but out of your budget, and will be on backorder for a while. Not a fan of HiFi Man's offerings, and the better of them (HE-6) have a much more limited choice of suitable amps as they require much more power to make sing. I'm not a fan of old Stax at all, but the newer stuff they've put out when amped well is excellent (007 and 009). All way over your price range though and you may even prefer Audeze, or at least wonder why people are willing to pay so much more for Stax.
As far as having "the same level of musicality"...well, OK, but don't expect them to be speakers. It is a different experience of enjoying music. It will never be speakers though. Then again, you may enjoy it even more, certainly some seem to. I'm not one of those, I much prefer speakers, but when privacy is necessary, the option is certainly nice to have available.