How should I select elastic for a sewing project?
This is commonly called the "stretch percentage" or "stretch factor". The name comes from how much percent of the original width/length the material can stretch. For example, if you can stretch a 4" piece of elastic to 6" long, the stretch percentage would be 50%.

Here's a simple visualization from Patterns for Pirates:



As a side note, some patterns come with a "stretch gauge", instead of telling you a stretch percentage. It's usually printed on the back of the envelope so you can easily measure your fabric against it:



What elastic to use really depends on your particular application! A thicker or wider elastic may be more sturdy but less comfortable, for instance. As a general rule, thicker elastics seem to be less stretchy - but it's a very general rule. If you know the measurements you want for the finished pants, you can come up with the required stretch percentage: (fabric width / fitted width - 1) and bring that gauge to the store to find which ones are suitably stretchy.