Twenty ten or Twenty eleven as base for responsive child theme

Both Twenty Ten and Twenty Eleven are being maintained, since both are still bundled with core. However, Twenty Eleven has newer functionality, and a better overall codebase.

I would recommend using Twenty Eleven. The only reason to use Twenty Ten, really, is that the codebase is considerably more simple.

Note: when Twenty Twelve comes out, I would recommend using it. It will focus more on simplicity, and will have some responsiveness baked in.