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>I'm wondering what's the point of it, besides cheaper accommodation.
I'd say college choice matters much more as an undergrad mainly because much of your teaching and support services are organised through college rather than your department/faculty. As a postgrad you have more freedom to have as much or little to do with college as you like - some/many colleges offer postgrads accommodation either on-site or off and you can choose to eat in hall, use the bar and MCR (grad common room) facilities. On the other hand there's nothing to stop you living in private accommodation and being more self-contained, in which case your choice of college only matters insofar as dealing with admin matters.
Obviously, the old colleges with the pretty buildings and central locations receive a greater share of applications so they often reject perfectly good candidates on that basis. If you plan on living in college and using student facilities then I would strongly recommend visiting a few colleges as the facilities can vary considerably - and as you mention, so does the rent they charge. Otherwise if you don't want to have much to do with college and just focus on your faculty, choose one of the modern colleges on the outskirts of town as they're much less likely to reject you.
Out of interest, are you starting a Master's or PhD?