A fair immigration policy for US citizens would take into account the effects of immigration on them and also take their concerns into account --with rigorous studies, not just cherry picked ones (higher income immigrants, for example, contribute more to the economy than unskilled immigrants, irrespective of country)
That said, to be fair to all potential immigrants, we should grant all of them equal potential access (i.e. someone from South Africa having the same chance to legally ingress into the US as a Canadian or Mexican who are right next door --it might also take into account their population, so someone form Indonesia has the same odds as someone from Belize.
And, to be fair to the American population, we should ensure those who come here are here to fill gaps in our society --so ensuring they don't undercut Americans jobs (that is let meat packers have to pay $25/hr to get locals to do that job rather than say have them say that no American wants to do that job. I'd bet many poor whites as well as many poor blacks would take those jobs at those wages.
Also, any underdeveloped population which moves to the US (or Kuwait or Chile) will typically increase their own per capita consumption (from a global perspective) also if they come from a country wallowing in economic mismanagement (say Albania) allowing Albanians (or Georgians) to flee means even less stability for those locales as it takes their motivated people and transplant them into a place that doesn't need them as much. There are many incidental things which a policy can affect. We're not a nation of 120 million or 200, we're at 330 and climbing and most with a voracious appetite for consumption (including the fast learning newcomers).
That said, fairness in immigration should be a priority rather than just allow those who runt the gauntlet successfully. And in addition, tie it to the ease of Americans's ability to migrate into these other countries, if we choose.