Automating jobs on the go

I want to learn how to write small, customized programs (scripts I guess?) that can be popped out in a minute or two to automate cumbersome or annoying tasks as they come up. Things like searching and renaming large batches of files, keeping tabs on a web page and logging changes, pulling out text of specified format or content from a database or highly-formatted source, etc. It's most important that these things can be made and run on any given Windows machine (think fresh install), with OS X and in-browser support being lower priorities. Mobile OSes aren't important.

Given that aim and those criteria, in which language should I learn how to do this and why?

You could try PowerShell but it's a piece of shit.
There's also Microsoft's POSIX utils thing that I can't remember the exact location or name for, and it might give you a few UNIX-like tools that you could use instead of having to install Cygwin.