You should consider:
Takstar HI-2050 (u$s 64)
Clearly on the bright side of neutral but still precise and definitely a top pick for the money
AudioTechnica AD900x (u$s 180)
Sennheiser HD598 (u$s 190)
Smooth and forward, not as bright or detailed as DT880 or K702, but more forgiving of poorly recorded material. Wide soundstage.
Beyerdynamic DT880 250 Ohm (u$s 220)
Slightly bright, with tight bass, good soundstage, and fast decays.
AKG K702 (u$s 220 - 240)
Wide soundstage, just a tad less bright than DT880s with more forward upper mids.
Sennheiser HD600 (u$s 370)
Smoother, not as detailed, not bright, regular soundstage but great tonal balance.
Bolded headphones need extra amplification to sound good. I'm not sure about the output power of behringher ha4700 units or avid HD.
Takstars are great headphones for the price, but probably not on pair with the others in this list.
AD900x, HD598, DT880, K702, HD600 are all very good headphones and most of the times the right choice is down to preference.
Best Luck!