This is one of the most important questions you could ask when looking for a tenant. There are tons of people out there, and many of them are looking for a home/apartment to rent. You want to make sure you don't just rent to anybody who asks. As for the "perfect tenant" they are not as uncommon as one might think.
Some advice I could give you is simply through the type of application process I have grown accustom to. There are many different aspects of a person to consider, sometimes it's not as easy as going by numbers and you'll need to look at it on a case-by-case basis.
Some of the aspects to look at are:
-Get a credit report (not just score, but find out if they have any collections, etc.)
-Check their criminal background (some credit reports will show this, but others don't)
-Verify their income (run the numbers in terms of their income, the rent you charge, their other current bills, etc.)
-Do a rental verification check. It is always a good idea to find out what kind of tenant they were at their last place.
These are just some of the many methods we use to scan tenants in order to find that "perfect" one. If you have any other questions about this, please let me know!