I own some pretty pricey headphones (Grado PS1000), some moderately priced (AH-D5000, Sennheiser HD595), and NUMEROUS Bose Triports (all broken/worn down). I used to listen to cheap $20, oblivious to some of the amazing stuff out there. Then I ran across some Triports, and I thought they were absolutely amazing. From there, I kept upgrading and upgrading.
This is my opinion. Remember that headphone preference is subjective! I believe the headphone sweet spot price range is around $200-300. Anything after that, and you're spending megabucks for small differences. Pretty much all of my friends can't tell the difference between my PS1000 ($1700 cans) and my Denon D5000's (~$400), except for the bass! They all prefer the D5000's. Some of the headphones that lie in that sweet spot are Grado 225i/325i, Senns 500 series, AKG K701 (great for classical), to name a few.
Not a bad idea that you're getting a portable headphone amplifier. Some headphones have huge resistances, and are considered "efficient" headphones, like most Sennheisers. The HD650 Senns have 300 ohm impedance. The Beyerdynamic T1's have 600 ohm impedance!!! You'll want a headphone amplifier for these if you're listening through your portable music player or phone. Other phones have very low impedance, aka "inefficient" headphones. Big one that comes to mind are Grados. Grados pretty much have 32ohms across the board, including my PS1000's. You can actually listen to them at a decent level on an iPod or phone. Headphones with low impedance are easier to drive than high impedance headphones.
There's more to it when talking about headphone amplifiers. For audiophiles, the cheapest component in their setup are usually the headphones. $1000's of dollars can be spent on headphone amplifiers and DACs. You don't want to get caught up in all this unless you want to shell out the big bucks, haha!
I'm sorry I can't offer much of a suggestion for your price range. The one thing that pops into my mind are the Grado SR80i, but even those might be a bit over your budget, and they're open cans :X. Audio Technica ath-pro700 mk 2 are great, too, for the price. Great bass! Double your budget, though. Perhaps you can find a deal on these used. Good luck and happy hunting!