This is probably the most important part of your resume.
I would get pretty specific about where I want to go and what I want to become, but by doing so, you will turn off some potential employers. Even so, the ones who contact you will know they can offer you something in line with your goals. Additionally, a specific objective indicates that you have well defined goals and perhaps you are a person who will be determined enough to achieve what you set out to do. Which translates - if an employer gives you a goal, you will also achieve it.