Well, you can get the 840s for $200 right now, same with the DT770s (80 Ohm or 250 Ohm) or DT990s.
I do know that the Beyers (those linked, anyway) will definitely benefit from an amp. A Fiio E11 would be enough, or an E07K/E17 if you want to use it as a DAC as well.
The Beyer COP wouldn't need an amp, and also falls into that $200 price range (though it's a bit more on Amazon right now, you could probably find it cheaper if you looked around).
I own both the DT770 (80 Ohm) and a pair of Grado SR225i, which are fully open. I listen to and love both. You would need an adapter for the Grados if you went that way as they only have a 1/4" plug.
I can recommend what I listen to based on the music I love; but that might not fit what you want. If you can, go into a Guitar Center or somewhere like that and audition a few pair of headphones to see what works for you based on the music you like. It will also depend on if you're buying these for music, gaming, or both. Trying them out will also help you identify features you might not like. I was dead certain I was going to get the ATH-M50s (another one in your price range) before I tried them out. They're highly recommended, but I didn't like the pleather pads on them. To me, the velour pads on the DT770s were infinitely more comfortable.
I was cautious spending the money on decent headphones too, but I'm glad I made the investment (especially after buying an amp and DAC). Good headphones and good source components will really help to make your music come alive.
Also, to add to a point about Fostex quality that you made earlier, the Fostex T50-RP are less than $125.
Edited by liquidzoo - 10/3/13 at 2:56pm