You don't mention how the power supply will be implemented. Battery is a great way to go, you get "free" isolation from ground. If you really want 0V volts output, you'll have to have at least a small negative supply or pseudo ground, etc- an amp powered by single supply can't make 0v- it can't sink.
You'll need to make a 10+ volt rail, 12-15v is convenient, you'll want a negative rail, perhaps -5v from a simple charge pump inverting the +5V. You could also use a pseudo ground scheme that used +5 and +17 say, and bring the +5 out as the analog common out as analog ground. This might make debug tricky with the arduino initially but you can work around this. For a decent portable instrument, you'll want low battery indication, backlight control (if applicable), auto shutoff, etc. You'll need to figure out how much battery you need based on your Icc's and conversion efficiency.
You'll have to look at PSRR to determine how quiet your rails will have to be- luckily the currents are pretty low so filtering won't be too difficult. I would recommend separated analog and digital supplies and extra care given to the grounding scheme.
The reference in the DAC you chose is surprisingly good at 2 ppm (typ, 5 max) for the B grade. A biploar precision amp would make more sense to give you low offset and offset drift. You might want to have a short circuit protection scheme if the op-amp's isn't robust enough. Bench equipment takes a lot of abuse.
Sounds like a nice project- good luck.