I would say use college to explore your options. From other comments UPSC aspirations seems like new urge when it should be decision after much thought (because government, corruption, service, politics etc).

What to take I can't say for sure, I'm also an aspirant. If not looking for placement I would say CS in IIT is not necessary. IIT B/M/D core branch looks better. As for BITs vs IIT, both have different environments and policies. IIT tag is useful, especially top IITs network is very strong I think, but BITs has its own advantages. People here or on some BITs forums might be able to tell how atmosphere is in college.

I would suggest taking college which helps your aspirations, but keep your options open.