Punctuation's advice is right on- read it thoughtfully. There is no magic combination. You are trying to demonstrate to the people who teach H & P at Oxford that you love their subjects so much that you have spent a lot of time reading around in them, and would be an interesting and engaged student to work with. The books, and what you make of them, are just a way for them to get a sense of you and how you think. I'm pretty sure that most of the tutors can spot an 'I'm trying to impress you' reference. And- if you get an interview you might have to talk about the book(s), so best if it is one that you genuinely found interesting and thought-provoking.
For the PS, tying the subjects together that you are applying for actually looks pretty straight forward - hardest would be St Andrews, but you have a very high likelihood of being accepted (early and with low or no conditions) anyway Work hard on polishing your PS over the summer- truly best to be done before school starts in Sept. Also, if you don't have somebody locally to review your PS (beyond writing quality, obvs), there are services in the UK who can help for a (relatively) small cost (about L50, I think, including review/revisions) that can some confidence that the style is in line with what the Oxford tutors would expect to see. There are several places- you can Google them. Also, get on Oxbridge Applications mailing list- they send a monthly e-newsletter with tips, etc (free).
The SATs seem to be used as a baseline or cut-off point, so don't worry too much about the 690M- I know somebody with your exact SAT scores (and many fewer total APs) who has an offer for H&P this year.
As other posters have noted, it is the APs are critical- and will be what your conditions are based on. Oxford will almost certainly ask for 5s on 3 relevant APs at the end of your senior year (in your case World Hx, Comp Gov, US Gov and possibly one other, b/c Comp & US Gov are lower tier APs). Btw, the girl with the H&P offer also got an offer from LSE for IR, but with slightly tougher conditions than Oxford- LSE specifically excluded the Comp Gov AP, Oxford included it! go figure.
As Sixdaysinthesun pointed out, April of your senior year- when your mates are all starting to chill out college wise- will be tough, as you have to sit all of the APs that you list on your application and you will need to make the specified 5s or lose your offer. (You can ask for an ok from your college ahead of time to drop unrelated ones, but word on the street is that they don't prefer that). And, of course, you have to balance out your US and non-Oxford apps.