Let's put it this way - you check references and if they qualify to rent (have an income), have good credit, etc. you rent the house out without discrimination on the basis of race, sex, or religious affiliation.
What I was wanting to know, since I've never rented anything to anybody, if you even suspect that someone wanting to rent a property from you is an illegal alien, can you decide not to rent to them on that basis, or do you have to just because they qualify in other ways?
Wow. That was a long sentence.
Well, not to get ahead of you, but you have to have a house in a good part of town to start demanding things like good credit. Some neighborhoods, you as the landlord are just going to have to take whatever tenents you can get, or let your property sit empty, because the folks with good credit are shopping elsewhere.