Printing on 1/2" cardboard counters

Does anyone know off hand how what kind of printing quality is available for a result to eventually be cut into 1/2" counters?

For instance: color, and resolution comes to mind, as does cutting tollerances. How close can I come to the edge before I risk the die-cut not lining up well enough and botching the job. (1/8"? 1/16?")

I'm concerned because based on the games I've seen, I'd have to guess that I don't have much to work with, but then again those were older games, and printing technology has increased quite a bit.

I ask here, because to find out, I'd likely to have to call dozens of printers for their capabilites. But if someone can give me a general idea, that'd be great.