Either way, I feel like doing a web startup would be a good way to learn firsthand bootstrapping entrepreneurship. And the skill sets (programming, rapid iteration, etc.) would be very beneficial in working on a medical device startup down the line. You're right about one thing - problems that need fixing abound in my field. I have a Moleskine with page after page of things that need fixing in the system!
You're in a good industry. Devices, especially non-invasive things, are the new new thing. I wish you well.