For me, the number one thing I look for is does it cast an arrow where I naturally look. Yes I can manipulate rest material, nock point and brace height, but there are jsut some bows that I pick up and no matter what arrow I put on the string (within reason) what rest material I use, what brace height, it just seems to work with my vision/face/anchor and puts the arrow where I look. I can't define what it is that makes this happen, probably a combination of things, but I know it when I shoot it.
After that I want a bow that is quiet, stable (I hate vibration in the limbs)and can cast a heavy hunting arrow with at least 175 fps (10-12 grains per inch).
For me this seems to be JD Berry Bows, my Thunderhorn 3 piece, and my Bruin Recurve.