I recommend Politifact and snopes, as they have business models that depend on getting it right. You can also pull up raw numbers from the Us census. One very basic thing is, if an article you are reading does not present the other side of the argument, you may be reading a biased article.

"the illegitimacy rate has tripled since the War on Poverty began" <--First, what do you mean by 'illegitimacy'? Second, correlation does not mean causation. This neglects all other factors at play. It sounds like more republican propaganda. Many of the wealthiest people in this country would love for you to believe that we should stop helping the poor so they can get a tax cut. Why would federal aid for the poor (welfare) be a bad thing for someone who lived in the inner city? 

Since the 80's income inequality has grown to record levels. Inequality is worsened by forces of capitalism, tax cuts for the wealthy, and reduction of aid to the poor. <--all things the Republican party pushes for.