With a US account, you will need a US billing address and payment method, and you get access to the US App Store for US apps, and access to the US iTunes Store for US content.
With a Danish account, you will need a Danish billing address and payment method, and you get access to the Danish App Store for Danish apps, and access to the Danish iTunes Store for Danish content.
You can change the region of an account, but it requires canceling all subscriptions. If you make purchases for content or apps, then those may not work after the change. Change your Apple ID country or region - Apple Support
If you set up two accounts, then those will stay separated forever.
So it largely depends on the duration of your stay if it is worth the trouble to set up a US account at all.