Honestly, I think any sort of skill at all would do. People holding a college degree or certification of mastery of some skilled labor or anything else would be a positive addition to our society. We're probably fine in the "people who can push a broom" category, though. It would only involve normalizing our immigration policies to those of most other countries. Intra-EU aside, most other countries aren't falling all over themselves to get as many of the unskilled, "immediately dependent on the state or crime" class of immigrants as possible.
This is (one of the reasons) why the idea of amnesty for current illegal immigrants is so backwards. Highly motivated people with money and PhDs take many years and tens of thousands of dollars to (sometimes unsuccessfully) get citizenship, but people with no skills, money, or education slip across a border (thus breaking laws in their first steps on US soil) and we'd give citizenship to them? Exactly what sort of society are we trying to build here?