There are are a lot of different things that come into play in deciding who to see first.
1.) If you have Insurance then you need to see a Doctor first and then get reffered to a specialist. This will insure that if your insurance covers the specialist that your insurance will pick up the tab.
2,) How were you hurt. Was it a quick injury, such as a sports injury, auto injury and some work injuries. In any quick injury were the injury happens in seconds or there is large impact such as in a bad car, truck or auto accident, fall etc... then getting checked out by a Doctor is advised. A chiropracter with an X-ray machine might do the trick too.
If the pain is coming from an old injury that has flared up or you slept wrong, worked out to hard, or some other slow onset then a massage therapist might be the place to start. Massage therapist work on relaxing soft tissue, Chiropracters work on the bones, Physical Therapist main thrust is building strength and conditioning, Medical Doctors main thrust is in finding diagnos and then helping to get proper treatment through any of the above treatments and others.
The most important thing is to remember that your the only one that lives with the pain and your the one who needs to get educated so that you can better direct your providers who ever they are.
The best time for a massage after a quick onset injury, such as, auto injuries, sports injuries, falls, etc... is as soon as possible after the inflamation goes away. This is usually 24-72 hours. Why get your massage so soon? If you wait to long the muscles shrink and harden making the healing process take much longer.