There are many different mobile companies around who offer all sorts of services including pay as you go handsets as well as contract based mobile phones. If you want to get top of range mobile phones at the lowest possible prices or even for free depending upon the package you subscribe with, you may want to consider going for a contract based service.
If however, you would like a handset that does not have any strings attached with it and if you would not like to affect your credit rating then you should be going for a pay as you go service but the choices of handsets would be limited and determined by your budget as you will have to pay for it in advance.
The advantage of going for a pay as you go service is that, you can get your phone unlocked to different networks and hence it would then just be about going for any network or even multiple networks to use with the same handset. If you were to go via the contract route then you would have to wait till the contract period expires before you could unlock your handset.
By researching mobile companies also known as mobilselskaber in Danish, you would be able to grab yourself the right deal.