A modern Danish kitchen would be high gloss white with hidden handles and a black countertop. Appliances is often concealed behind cabinet doors for a sleek look.
I am more traditional and have chosen a birch kitchen from IKEA with a custom oak countertop. IKEA generally have a better reputation in Denmark than in the rest of the world. Their kitchen elements have the same quality as other kitchen manufactures, only the number of options are lower than the competition. An IKEA kitchen would be the DIY person's choice; they are very easy to assemble and you can pick them up in your local IKEA from day to day.
Also notice that there are no cabinets (apart from the sink cabinet) only drawers. Cabinets disappeared from the modern Danish kitchen about 15 years ago because it is easier to retrieve items from a drawer.
We have no cooking range either. Our preferred design is an induction cooktop and a wall oven. This gives no gap between the cooking area and the countertop.