I’ve just finished my first term of PPE at Oxford. The single most important factor in terms of deciding who gets invited to interview is the TSA - really, I cannot stress the importance of getting as good a score as possible enough. FWIW, I started working through past papers in September, so around two months before I sat the test.
Seeing as you’re still only at the beginning of year 12, you really don’t have to be doing anything yet, but I’ll give you this advice for further down the line/if you really want to start early. Read around the three subjects, especially areas and subfields that particularly interest you (but really there’s no need to read loads! Certainly never let it distract from your schoolwork). The three subjects are really very different (and by all accounts much more interesting!) at uni compared to at A level (I didn’t actually study any of them), so stretch yourself beyond the confines of the syllabus to get an idea of what studying them at uni will be like. In addition, the best thing you can do to prepare for the interview is to get used to verbally expressing your ideas and arguments, so try to discuss the subjects with anyone you know who’s willing to.
Regarding the personal statement specifically, Oxford barely care about it (it only ever came up as an icebreaker in one of my interviews), but LSE really do.