At that price you won't be able to put an Opus build together, nevermind a built-in headphone amp, so scratch that idea
.
I think you'll probably have to forego the S/PDIF idea then too, since that will significantly complicate the DAC design (you can't just use a single chip as DAC and USB receiver anymore), and I don't think there are any readymade inexpensive designs to do this. That means you're left with something PCM270x-based like the AlienDAC, which is a good DAC in its own right, and it's the same chip used in the Fubar. A kit from Glass Jar will run you about $50.
For the headphone amplifier, I think the
PIMETA is a good choice for you. It's a three-channel (active ground) opamp-based design with IC buffers on the output, and there are lots of 'tweaks' you can do to the basic design later if you lust for more quality. One issue with this design is the buffers, which are difficult to source right now. You will need to find a replacement, either a discrete implementation, like a 'diamond buffer' board or a similar integrated chip like the LMH6321, but this may require minor modification. Per-Anders sells the
QRV05 board that is supposed to work well, but the SMD might be a bit challenging for you, and it'll drive the price up), and I believe the JISBOS kit from Glass Jar would work well too. Depending on how you choose to do it, the PIMETA build can be as cheap as $100 to probably around $300.
You might also like the
M3 from amb, which has an opamp input stage and discrete MOSFET outputs. It'll be more costly than the PIMETA, probably out of your budget, mostly due to the more elaborate power supply and larger case required. It doesn't have the issues with part availability that the PIMETA does, or the same tweakability, but it is an excellent (probably better, IMO) design and powerful enough to even drive some small speakers, and it's designed to be a desktop amp, while the PIMETA aims for portability. A basic build should run you around $150 for parts (plus shipping).
You'll need bipolar power supply like the
σ22 from amb (Glass Jar has kits at ~$100 including transformer). If you can get ahold of Russ or Brian at Twisted Pear, they might sell you one of their LCBPS kits separately which should be significantly less expensive and would work well.
Don't forget to budget for the casework, which will be a significant part of the cost. You'll probably spend about $50 on the chassis, plus probably $15 on a volume control and $15-20 on connectors. Add hookup wire, a power switch, power inlet module, screws and standoffs and you're up some more. If you go the M3+AlienDAC route, you're probably looking at $300-400 all told for a budget minded build. The PIMETA is probably a bit less, but not that much, maybe $250-$350.
Just a couple ideas, there are lots of choices, at least in the amp section.