Hi

I've been using K2 for years with a basic information site but now want to set up an online magazine. I was going to use InDesign to make an epub but have come around to thinking that a responsive website using K2 would be a better move. However, I want to have the current issue, and previous issues, available to users. Each issue should look as it did when it was created, not a list of archived items.

Is this possible and if so what is the best way to structure my categories to make it work?

I would suggest that you download a template quickstart and see how K2 is set up.
You can try Takai which is free and has a magazine look and feel www.joomlaworks.net/joomla-templates/free-templates/takai

To be honest without further information it is impossible to give you any further info.