As I've mentioned on the other thread and as someone have pointed out above, the US already has a base and a number of dormant bases on Greenland. Denmark is quite happy for the US to "staff up" all these bases or even potentially create more (it is in a 70+ year old agreement). The US does not need to "own" or "control" Greenland in order to have whatever military presence there that it wants or needs. US bases all over the NATO region have operated successfully on exactly this principle and have done for decades
The Danes and Greenlanders are also more than happy to "do business" with regard to the minerals there - there have been business discussions between US and Denmark for many years on this . . . why wouldn't Denmark/Greenland want to sell minerals or mining rights to the US? The problem here is accessing those minerals due to the geography and climate.
I believe that this threat of "taking" Greenland is probably Trump's vain desire to be one of only a few US Presidents who have increased the area of US territory (Think about his obsession with Obama and his Nobel Prize).