I own a C-One myself (seeing Minimig fire up and play Battle Squadron was a rush like I hadn't expected at all), but no matter how much I have searched the net I can't really find any hard data on what the video and audio can do.
The C-one schematics will probably tell you more than anything else: http://c64upgra.de/c-one/
Sound: KHz? Bits?
At a quick glance, it has an lc78835m DAC - so check out the specs for that?
Video: Resolutions? Colourbits?
Video looks like a simple R2R ladder, with 16-bit (5-6-5) colour depth. The rest will be implemented in the core itself, so the maximum possible resolution depends mainly on available RAM bandwidth.
I was hoping to pick up some Verilog by messing with the sources. Doubling up sound to 16 bits or 56KHz sounded (badoom-tisch!) like something small enough to try?
Nice ideas - the only complication with those is that sound on the Amiga requires DMA, so making a change that doubles the amount of data required is trickier than it sounds!
What might be a better first project is maybe to add a new custom chip register that does something simple like maybe double a value written to it, then progress from there. Maybe create a "hardware assist" for something that's normally very slow on the 68K processor, such as calculating a Mandelbrot set? Or JPEG or MP3 decoding.
Either way, you'll need to write some software to go along with it - but you should at least be able to see your tinkering having some effect with something as simple as peeking and poking in AMOSPro.
Another thing that could make a nice project - though I don't know enough enough about the C1 - would be to expose the SID chip registers to the Minimig core (Assuming it hasn't already been done. Again, custom software would be needed, though.)