To hopefully clarify a bit (since the installation messages are definitely not the most user-friendly), this line:
means that stringi failed to install (because, in this case, you were installing from source, stringi needs compilation, and it failed to compile). That's why you keep getting error messages about stringi being missing.
As Mara said, if you haven't installed RTools before, you will need to do that if you want to install packages from source that need compilation (these are ones with C++ or Fortran code). But if you want to try to quickly get moving again, you can see what happens if you install the older pre-compiled binary version of stringi (run install.packages("stringi", type = "binary"). It's possible that there will be incompatibilities with the packages depending on stringi, but this can sometimes be a useful stopgap.
You might also want to check out the installr project, which tries to make package installation on Windows easier: