The reputation is brilliant. CLC would probably get you anywhere if you want to apply for internships in places like JP Morgan and Goldman.
Most of the teachers are good at their jobs. They will push you and push you until you're dead tired, but you'd probably get the results you need to get into a good uni. If you're a humanities and art person, CLC would be great. Sciences...you get good teachers, but it's more of a hit and miss thing. because good teachers are brilliant and the bad teachers are crap. The history and politics department I'd say would be one of the best ones.
If you hear that students are posh and arrogant, it's probably from someone who's not going there. They can be to outsiders who are not from public schools, but among themselves, they're normal. And of course the reputation of Second hand virgin megastore. The only thing I can say is, every school get their own sluts. They're not as desperate in sixth form than when say, 3s-4s. Although I must warn you, they can be really naive in the way that they're stuck in their own world. They don't get to experience outside things a lot, sometimes to the point that non-wealthy families are like a myth to them.
Houses would probably grate on your nerves a bit when you start, but you'll get into the routine soon enough. and of course there are the boarding restrictions. Internet for one shuts of at 11pm everyday and no facebook on weekdays.
Cheltenham is big for a town actually. I've been there for six years and by the time I left I found it boring, but if you're apply for sixth form, you'd probably be fine.
If you have any more questions, you can ask me. I just graduated there last year, so I can't be that out dated.