You will have plenty of stuff generating noise well into the 10s if not 100s of MHz. Not only the PIC, but the bit clocks for the ADC and DAC. In addition, your ADC is capable of 24 bit resolution, although you'll probably only realistically get the equivalent of 18 to 20 bits if you're lucky however you roll it. Even at 16 bits with 3Vpp input, that's a resolution of 45uV. It looks like it may only be single ended too. It doesn't take much to induce a millivolt let alone 45uV.
I am sure there are many ways of approaching this. Ask three engineers the same question, you'll get three different answers. As I mentioned, I do use breakout boards for prototypes despite knowing it'll be sub-optimal in the analogue domain just to resolve any functionality problems before laying out a board... or even a schematic! Sometimes I might unit test a particular area on PCB right off the bat, but at's usually for controlled impedance stuff or high speed opamps that love to oscillate given half a chance. I am sure in other organisations that aren't one man bands there will be a guy to do the schematic, someone else to do a board layout etc etc.
If I do layout a unit test board, then I will always make the board myself too: waiting for boards always ruins my workflow. Only when I have everything unit tested and system tested as a whole perfboard/breakout board/mini PCB do I lay out the final schematic and board and submit it to a board house. It never works 100% first time for me, there's always something, but if I'm lucky I might get away with just one more spin.