Krugman explains the basic textbook reasoning for why an economic stimulus should be focused on lower income individuals.
Another good thing to do would be to fund productive public infrastructure projects. The downside of doing so would be that such projects can take time to plan before the money already gets spent, though there are plenty of projects that are essentially just waiting for funding. The upsides are: presumably a lot of jobs being lost are in residential and commercial real estate construction, and increasing public infrastructure expenditures would provide a jobs cushion for those people; there are a lot of crumbling bridges which need to be repaired as there's been a lot of absurd and ultimately costly "deferred maintenance"; smart projects will have later benefits.
Along those lines, Fred Hiatt is shocked that insane conservative free market ideologues like the ones his paper publishes on a regular basis actually mean the things they say!