The application process is pretty straight forward. Look up their visiting students page. My advice would be to invest the time and money in clinical work than do research if you are just doing it for your resume. Most people do it for 9 weeks which is pretty short period of time to get any real work done. You can always extend once you're there but even with all of that getting work done as a first author is pretty rare. Most people end up getting published as co-authors, not even second, which is not that worth it. But you might get a good LOR and if you're really interested you will learn a lot. As far as the PI you mention on your application goes, it should depend on your interest. You can choose people who do basic science research or people who do clinical work. That is upto you and your choice should depend on your long term goals. If you are on the fence about research doing clinical work and developing contacts that way in places which you might match is a better option. Also, high score + good clinical experience beat research electives any day. If your long term goal is to stay in academics and do research than apply for an elective to get started some where. You could try mailing attendings and show your interest to increase chances. Good luck.