Earlier quoted context omitted.
You always need to balance Precision and Recall. For something like this, you want to be exhaustive. I've worked on search engines, and depending on who is using them, that balance gets struck differently on the ROC curve. For legal matters, for example, they want every record that might match. For ad-hoc (google style) queries, nobody reads the second page so you care more about Precision @ 20 (or really, at 3)
Somewhat offtopic, I'm curious about this "nobody reads the 2nd page" meme... I find myself reading pages 2-5 quite often, because page 1 just didn't give enough results, and I doubt I'm that much in a minority ? (I'm talking about actual generalist searches, not people that use a global search engine as a replacement to bookmarks or directly searching, for instance, Wikipedia.)
And many queries that are solved with 0 visits, thanks to the information being pulled out from the wiki, or giving up and rephrasing the query.
After those, then yes, most queries will be answered by the first page. It's what retrieval is optimized for.