Oxford colleges offer places based on the assessment of academic potential, and the likelihood that a candidate can do well in the tutorial system.
The workload at Oxford is high, but not so high that students cannot relax and have fun.
There is no prejudice against private school students. The supposed prejudice is a myth spread by the media and by disgruntled applicants and their parents. Private school students still obtain approximately 30% of the places at Oxford, despite being a much smaller percentage of school students across the UK.
Oxford colleges are not interested in a candidate's extra-curricular activities, but may be interested in super-curricular activities. They are interested in commitment to the subject, and signs of reading and thinking around and beyond the courses taken at sixth form. Success in music or sports, being Head Girl/Boy, and all that sort of thing, are of no relevance to the Oxford admission process. That is not to say that such things are not worth doing in their own right.
A successful candidate will have good predicted or actual grades in A levels or the IB, a good personal statement, a glowing reference from a teacher, will do well in any subject-specific aptitude test, and will perform well under pressure at interviews. GCSE grades are of lesser importance, but good grades do no harm.
For humanities subjects, social sciences, and life sciences, there is no need to take four A levels unless you really want to. A level law is frankly a bit of a waste of time.
Please do not obsess about choice of college. There are no bad colleges at Oxford. Most people who go to Oxford end up loving or at least liking the college they go to, and many develop lifelong affection for their college. A successful applicant may be offered a place at a college other than the college applied to in maybe 25% of cases.
Oxford does not work for everyone, Some people don't like it and drop out. Some finish the degree but can't wait to leave and never go back. The dreaming spires can make dreams come true, but not in every case.
Oxford does not always give you a golden ticket to a perfect postgraduate life, but the education, more than the name, can enhance your chances of finding a job that makes you happy, regardless of how well or badly the job pays.
Good luck!
Miss S Byng MA (Oxon), barrister.