There's no doubt that every property does not fit a tenant's needs when they're looking for their next home, but the reverse is true as well. Not every tenant fits the property. While you do not want to accept a tenant that you will constantly be clashing with and that has little to no respect for you or the property that they're renting from you, as a landlord and property manager you will need to be very careful on how you go about your screening processes. There are questions that you may not ask when trying to get a feel for the person showing interest in the property. There are federal laws that dictate what is considered discriminatory questioning (asking a person their martial status or their religion would be an example of two, though it's certainly not limited to that). You may not want children running around your rental, but you cannot choose not to rent to a qualified tenant strictly based on her family status. This would be considered illegal. Now, if more people are asking to move in than is safe for the size of the property, this could be a different issue entirely.
Always check up on your local and federal laws to make sure you're up-to-date with them and not inadvertently showing prejudice to one class of people over another. Currently you may deny a person based on their smoking habits or if they plan to keep a pet (unless it's a service animal ) in the home.
So what are some ways to encourage the kind of tenants that you would like in your apartment? Likely you'd like a tenant hat pays rent on time, keeps the property clean, does not break the law, and does not disrupt their neighbors. One of your very first steps will be to look at where you're buying the property. While obviously not everyone in a high-crime neighborhood is going to be involved in illegal activity, you'll raise the odds of having someone with a criminal background if you want to buy a property in an area such as this. You'll also limit the people that are willing to live in that area as well.
For tips on how to find terrific tenants, check out BiggerPocket's article here