if you already have finished you study, you should apply for membership as an employee.
(I assume you have work)
Because you are an academic I will advice you to choose an A-kasse (Unemployment fund) targeted academics.
As a guideline you can use our guide for students because its the same A-kasser that focus on academics.
Find them here: http://a-kasser.dk/students/
At the page we mention 5 A-kasser and the degree courses/academics they are associated with.
You can also try the drop-down on same page, but only if you know what your education is called in danish.
If you dont care about haeing an a-kasse targeted academics you could also just apply for the cheapest A-kasse.
Its called FTF A-kasse. You find link on our page. You have exactly the same rights about unemployment benefits, no matter what a-kasse you choose.
If you have not finished study you can apply for FREE membership.