How should a society primarily take care of its poor?

The idea that poverty can only be fixed with money (and education) is a serious (and almost insulting) misconception. People need a sense of direction and the feeling that they can rely on something (/security) when their future is uncertain. Wealthy people aren't (usually) wealthy by accident; they made it happen.

It's a difference in attitude of mind (although of course I should add that I'm currently generalizing, as I haven't ever visited these counties, have little to no knowledge of US tax rates or the conditions these people are living in).

"Poor people" (people with incomes that don't sustain their basic human needs) need help, but mostly they need to feel taken care of (in an un-patronizing manner) and feel accepted within the community. To propose a concrete idea (shoot it down if you will <- or perhaps this already happened): the state should finance the county to literally clean up the streets, restore buildings that are valuable to the community, issue orders for agricultural maintenance (perhaps with the aid of low-level crime offenders), and just make the county a pleasant place to live in that's worth working for.