Hi, I'm also applying to PPE and from my understanding after a fair bit of research:
As far as PPE
courses, Warwick and UCL are extremely highly regarded. The former is probably the best
interdisciplinary course because far more than Oxford it stresses the links between the two, and UCL's PPE course has a really strong policy and quantitative focus. LSE course-wise is not famous or anything, but LSE as an institution you go for the name. You get a degree from LSE and you'll have no problems landing a job so it doesn't really matter, I mean no one goes to LSE for the student satisfaction, contact time or great social life because...well...it usually lacks in all three...
KCL is the least regarded you've listed unless you're thinking about getting a job internationally, which KCL has a great reputation for mostly because it's in London. But even if as institution/course domestically, Durham does better (largely because the uni itself is usually academically stronger), but even York does because its PPE course is older and more well established than most of the listed options, even if as a uni it's usually lower down. I guess just for completeness sake, domestically a PPE degree from Exeter would be highly regarded too. Of every uni I've listed: Oxford > Warwick > UCL > LSE > Durham > York > KCL > Exeter would probably be correct.
Yeah as far as the course, pretty much anything from politics to finance. With PPE most fields people go into don't require absolutely specific degrees, but a background in politics and economics opens up your options quite a bit. More important is work experience, contacts and the university you go to but the transferable skills you get from a PPE course are really useful too. From a good uni, a PPE degree is not a disadvantage in any sector you listed.
Hope this helped
Edit: I guess though just a point on reputation, a York PPE degree is better than a KCL one, but only if the employer knows that which you can't guarantee, and if they don't KCL looks better. If you're applying for finance, reputation and universities are far more considered but with PPE being so broad, the usefulness of the reputation of your uni is hard to say for sure.
I'd give a different ranking for quality of the course, but that's a lot more subjective. From any of those unis it won't be a huge problem so pick the ones you like. Durham, LSE, York for example don't give you the option to drop one, but the others do. As I've mentioned, Warwick is a lot more interdisciplinary, and Exeter in general is really flexible. Find the course you enjoy most, from any of these unis finding a job should not be a problem provided you do well, get good experience, etc.