Yes. If you have a valid passport and either a valid residence permit for a Schengen country or a valid Schengen visa, you will not be needing a visa for visiting Denmark.
You are not free to apply for the Schengen visa for any country, you must apply in the mission or embassy of the country where you are planning to stay for the longest duration. If it is difficult to determine this, especially if you are taking a cruise or a bus tour, you can apply for the visa for the country which is the first point of entry. This is provided you are spending equal number of days in all the countries.