Should I do internship or a job to utilize my time? Does it matter if my internship is paid or unpaid?

It matters a lot. Whether you are in a job or in an internship, you must be paid for your work.

Well, internship or job, anything which is available is better. Coming to paid or free, I would suggest you not to go for free internships as your effort is being used by them. At least, you must be able to earn something just to sustain your life. Getting paid for our work is our right.