As for goals/uses... really I just want options. Ideally in the future I can interface between arc and this/these languages. This way if arc is not a good fit for doing some thing then I can use another language to do that part.
Then I look for libraries or API's that will do that thing for me.
If there are several options, I look for one which seems to be the most practical and straightforward implementation.
These days when I go through this process I most often end up with a library or API written for Perl, Python, Ruby, or Java.
What I would suggest is learning enough of each of these languages so that you can make library calls. Which is pretty easy to do; you don't need to learn a lot to do that.
Then how much you need to program in that language vs. Arc usually comes down to efficiency. Each call from Arc to the other language involves a round-trip of some sort; so if you're doing something in a loop then you'll often want to push the code to do that loop into the other language. So you may end learning more of the other language as you translate some parts of your Arc code into the other language.
