Regarding jobs you are not qualified:
Yes, you should apply. Usually in a job description there would be a lot of requirement but it doesn't mean that if you don't have all this skills they won't hire you.
IMO a good rule is : if you have 60% (or more) of the skills you should apply.
Regarding jobs you are not interested:
Why are you not interested? Because of the skills required? The level of the position? Because the company is too big( or too small)?
I suggest to apply to every jobs that seems in your reach. A job description is not everything, meeting the people you will work with ( especially your boss that if your are young can become a mentor) is also very important.