I'm looking for a physical learning resource that contains the basics of multiple languages (I don't care which), so that you could get a sampling of several different languages. Ideally this resource could be used to evaluate basic grammar/vocabulary of a language; if the language learner wanted to learn more, they would of course seek out resources dedicated solely to that language. Does any such resource exist?
This--The Loom of Language by Frederick Bodmer--is pretty close; even if it's not exactly what you were looking for, it's still a fascinating and compulsively readable resource. The "Language Museum" at the back kind of attempts to give you a working vocabulary in English, Swedish, Danish, Dutch, German, French, Spanish, Portuguese, and Italian at more or less the same time. I'm not sure if you will ever learn how to speak a single language from this book, but you might learn how to speak "language." (Or get some insight on where you want to go, if you think there's a good chance it might be Romance or Teutonic.)
The 50 Languages website contains a pretty large set of phrases translated into, well, 50 languages. It starts with very simple phrases and gets into more complicated ones, like in a language course. Books have been published for some of the language pairs, and if you need others, you'll probably have to print the relevant parts of the website on your own. It doesn't look like they sell CDs, but the audio files with the sentences are freely available, so burning your own CDs should be easy.
It seems that all the phrases have been translated from one source language, so you should keep in mind that sometimes the phrases aren't completely equivalent and there may be some variations in meaning. But it should work fine as a starting point for looking into these 50 languages.