Hi Zachary,
DO NOT ever target one page only. If you are really very very busy, please, optimize at least couple of pages. There has to be a diversity in links as well as anchor text. Of course, you will concentrate a little more at home page and main keywords but please remember about link and anchor text diversity.
As of the low-hanging fruit - absolutely NO. It's much better to build 10 good links than 1,000 spammy links. Google is smarter than this. Trust me, Google's thousands of engineers are working every day to improve search algorithm. You don't want to take that chance and compete with them.
Good luck & see you at the top