Sameera, did you test Twenty Twelve, and what did you learn? I have a similar requirement, but in our case it’s to provide resources to people who live in remote areas of Africa and Haiti, where bandwidth is typically 14.4K bps, when available at all. I’m just starting to think about this problem, and would love to know what you’ve learned.
One idea I had is to install Jetpack and enable Jetpack’s Mobile Theme feature, which delivers a lighter site to those on mobile devices. In many areas that we serve the mobile service is faster than the land service.