I really think the most logical way for a Greenland state would be in union with another region, being it Newfoundland and Iceland. Of these two, Newfoundland is possibly the easier one of the two to have happen.
In that case, it would likely have a few counties around Nuuk and similar where there are large populations, while the rest of the region is subdivided into larger counties, federal regions, military bases, reservations, and wildlife reserves. The population might get as high as 100k... Maybe... with military families living in the southern side or just back in Newfoundland. mind, the entire island would be autonomous in relation to Newfoundland as well, considering it's a separate region so far from the rest.
Not really much more to it. It'd make relations with Canada more interesting for sure(the Arctic treaties!), but it really only could come into existence much as part of another state.