I strongly recommend the JDS Labs Atom+ stack. The amp is $100; the DAC is $120. A smidge over your price range, but there’s ample, clean power for the Elegia and most other headphones.
The advantage of a stack over an all-in-one is that you can upgrade pieces individually. Want a different-sounding DAC? You don’t need to replace your amp, too.
But the advantages of an all-in-one are more desk space and fewer wires. Still, the Atom stack has a very small footprint.
One caveat: The case of the Atom+ amp and DAC is hard plastic, not aluminum or some other metal. It’s sturdy plastic, not cheap, and that decision helps JDS keep the price down on what is a superb-measuring DAC and amp. Thought I’d lay that out there, though, as the plastic build bothers some people. Not me! Love my Atom stack!
Edit: Oops. This is the second time I’ve recommended this stack in this thread. Apologies. I need to pay better attention to previous posts!