I have also just moved into a new apartment in Copenhagen and needed to find new furniture, including a bed. The cheapest and easiest option was to “buy” a used bed (buy is in quotation marks because many beds are either given away or cost a modest amount, as long as you pick them up yourself). The first bed I bought was too wide to fit through the stairwell, so I sold it the next day without any problems. The next bed (a futon in perfect condition) was easy to take apart and fit through the stairwell without any problems.

Compared to buying new, it was much cheaper, and compared to building it myself, it was both much cheaper and easier.