Italians can you recommend an espresso machine for me?

If you can afford it, get some entry level Gaggia espresso machine. For example Gaggia Carezza is a nice starter machine. You can read a review about it here:

http://www.espresso-machines-and-coffee-makers.com/gaggia-carezza.html

If that’s too expensive, there are some cheaper pump espresso machines – you can read about a few models here (not sure you can get these in Denmark though):

http://www.espresso-machines-and-coffee-makers.com/inexpensive-espresso-machines.html

If all else fails, consider getting Aeropress along with a decent grinder and you’ll get really nice coffee out of that.