Run R in emacs with ESS (Emacs Speaks Statistics) r-mode. I have one window open with my script and R code. Another has R running. Code is sent from the syntax window and evaluated. Commands, output, errors, and warnings all appear in the running R window session. At the end of some work period, I save all the output to a file. My own naming system is *.R for scripts and *.Rout for save output files.
Here's a screenshot with an example.