You can almost take it for granted that an Oxbridge applicant will have the relevant predicted grades and work experience. As for the actual college, if you decide to indicate a preference, make sure you have done some research and ideally visited the university, as you are highly likely to be asked about your choice in the interview.
Each medical school has its own criterion for evaluating a candidate’s personal statement. It can be used purely as a tool to decide who to call for interview, and therefore which applications to reject. The medical school may use the personal statement as a proportion of the overall assessment process (for example it forms a certain percentage of your overall assessment, combined with a score for interview, examination scores etc.)