I highly suggest you intern (paid or unpaid, depending on your financial needs) during the school year. Assuming your schedule permits, and you are able to balance your school and work responsibilities, I think the balancing work and school life will give you a skill-set (juggling life), that you can only get through hands-on experience (and not something that is learned in text books). And of course, you will benefit in other areas from completing an internship, like exposure to work life, developing professional connections, learning from professional in the field you are interested in, etc. Either way, there are a lot of benefits in doing an internship, so whether you intern during the school year or during the summer, I say just go for it!
Your college years and entering the work force is a very exciting time. I wish you all the best- good luck!