A web interface to an R program [closed]
R has its own web server, so you could do the whole thing within R. Then there's no need to bother with choosing a framework, or getting them to talk to each other and so on - just use an R framework:
http://cran.r-project.org/web/packages/Rook/index.html
If you don't like that for performance or other reasons, pretty much any framework will talk to R one way or another, so use what you are familiar with. I'd use Django and either call R via Rpy2 or run an Rserve process, but if you can program in PHP or Java then use a framework based on those languages. If you can't program in anything but R then either learn Python or use Rook.
Rstudio has a new server called Shiny which uses node.js for the UI: