If I were building a new system with that budget here is what I would put together:
Amp: THX 789 or LCX - both have pretty solid power, the former aims for very netural, the latter warms things up a shade, both should be able to handle a variety of headphones
DAC: SDAC Bal or SMSL SU-8
Headphones - Hifiman Ananda, Edition XX, TR-X00, Elex - nothing wrong with the 660S or 1990, outside of the Beyer spike in the treble region. I don't have any headtime with either, however I do own the 650 and 990 predecessors. The 990 is my least favorite Beyer and I've owned 4 of them.
My primary rig (and my cost): TEAC UD-501>Cayin iHA-6>HE-500/Elex/T1/HD650 ($1390 to 1860)
Reasoning: I prefer separates as I can swap a piece of the chain for something with different features without being forced to change other aspects. The Cayin works extremely well with balanced headphones, not so ideal with low-impedance SE varieties but I have other amps that are more of a "jack of all trades".