Self-employed tax advice

Hello, Forum dwellers! This is my very first post. Be nice.

So, this is my predicament. I am from England originally but have been living in Copenhagen for 20 or so months enrolled in a Masters at the central university. I am a fully fledged, yellow card waving citizen here.

I finish my education in October, but already have a job offer lined up. It's working for a media and music management company based out of London, on the annual income of 25,000 GBP per annum. They want to take me on as a self-employed contractor for the company. The nature of the work will see me travelling across Europe and the States for 5-6 months of every year, but they would like me to keep my place of residence here in DK.

So, here is the predicament I find myself in, in the form of questions:

1) Do I register as a self-employed/ltd company here in DK, or back in the UK?
2) How will I have to pay for tax, approximately how much I be paying, and to whom? (any clue on Double Taxation laws?)

I am quite adamant that I would like to stay in DK but, considering the travelling nature of the work, I may have to consider giving up my residency here in DK, and do everything above board in the UK. However, does anyone here have any experience of residing in DK but not as a fully fledged resident. For example, would it still be possible for me to have a Danish bank account and buy an andel here, if I decided to conduct my business solely through the UK; and would that mean I'd need to give up my residency here?

I appreciate that this a smorgasbord of questions in this post. I'd appreciate any advice or words of encouragement.

Thanks in advance. Be sure to enjoy this sunny weather.
Luke