Not easy to answer, as it is easy to question. Because, it depends upon all the competition, and how powerful the keyword is, I cannot say backlinks is the only result to get #1. You are not seeing how good content and how powerful it attracts people. Having on page seo, is perfect to get good rankings.
Comming to Backlinks, Make around 2-3 per day, and increase slowly, you do not need to even purchase backlinks if you are good making your own backlinks. Get .gov or .edu backlinks. They are so powerful, because you are getting popularity from recognized websites.