The sixth year is not an option at Brown and you should have a demonstrated interest in research if you are applying there. If that sounds ok to you, then you'll really like all the other great things about the program when you interview there.
In general, any third year interested in a program should email the program directly for info, then ask questions here that are still unanswered. Many programs will send you a folder of information and are very good about answering questions directly. I know this is the case at Brown.
Good luck and start early. That ROL deadline will start moving up quickly.
