I would prioritize the criminals thats for sure.
Its really easy to implement a cost effective (I bet it would save money from overstays, good investment) system that both discourages people to come here illegally by overstaying visa's and improve it. All they have to do is use a simple database and it would all be automated. Someone visits a country they check in through customs, get a stamps in their passport and they are logged into a computer. As soon as one overstays their VISA without asking for an extension, the automated system posts them as wanted by the F.B.I for immediate deportation and heavy fines imposed (well probably wont get much but more of a tactic, or seizing assets, etc...) and permanently be revoked visa rights for life unless a REALLY good reason comes up.
Put up a website, make their faces public.
How simple is that? You see, I should be President

And of course I would hire a private (American) company to do it so its secure and reliable.