Medical Science sounds like the kind of course you will want to do if you're interested in medical research. Actually most science degrees (whether it says medical science or not in the course title) at a decent university will lead you to a career in medical research. What you should watch out for is whether the university has the appropriate departments in order for you to do cancer/medical-related research. For example, a biochemistry department would be more suited for your interests than, say, botany, physics and mathematics, if you're interested in cancer research.
Farmers08's post above is only partially correct though. You will want to do a PhD degree (which is a step above a masters research degree) if you really want to get into the core of the research field as a Principal Researcher (ie. running your own research and not just being a lab assistant). Entry into a PhD program follows from your honours year (so it's bachelor degree --> honours degree --> PhD). Of course you'd have to perform well in your bachelor degree to be accepted into the honours program, and then into the PhD. Performing well in your honours year will help a lot when you apply for scholarships and funding for your PhD.
As for choosing a good uni, it's actually the quality of your research during your PhD that will decide where you go afterwards. And a good uni is a uni that can provide the resources and expert guidance that will allow you to conduct your PhD to your full potential.