The vast majority of property in Copenhagen consists of flats and apartment blocks. Apartments on the ground floor are usually the cheapest, while those on higher floors tend to be more expensive. Apartments on the top floor tend to be the most popular even though a lot of the older apartment blocks in Copenhagen do not have a lift. However buying any apartment in Copenhagen, no matter which floor, is always going to berelatively expensive.
If you are looking to buy a house rather than a flat you would be better off looking further into the suburbs on the way out of the city. Types of housing available vary from terraced housing to detached houses set in their own grounds.
There is still a lot of property development going on in Denmark and an increasing number of properties will be available in the near future. A major redevelopment project around Copenhagen is planned and they are extending the public transport system into the newly developed parts of the city.