Hi there,
The bad news is that there's no "right" answer to this question. Search engines only reveal so much about what goes into their ranking algorithms, so it's hard to say what strategy is the best one.
One thing that's for sure, though, is that you want to avoid Google viewing your keyword optimization as keyword stuffing. I would strongly advise against the second option you mentioned (optimizing for several different keywords), because that would mean you'd mention three or four different keywords multiple times, which Google might view as keyword stuffing and/or providing a poor user experience. Both of these things could result in lower rankings.
The safe, and generally effective, bet is to choose one primary keyword that's as specific and relevant to your page as possible while still averaging a decent monthly search volume, and back it up with a secondary keyword that's also extremely relevant but isn't your primary keyword because it doesn't have as high a search volume. That way, you'll draw relevant search traffic to your page without it feeling spammy.
Hope that helps. Happy optimizing!