James, be very careful here. Your statement that "We liked almost all of them" is very dangerous and irrelevant. You are looking for superior QUALIFIED applicants, not people you like. Felons and professional evicted tenants may be very likeable but you do not want them as renters.
Are you charging an appropriate application fee for each applicant?
Like the other posters said, use the LPA pre-screening card info and ask all these questions up front, before wasting your time on a showing or taking applications.
Last year I processed 150 interested inquiries, but only found 3% of the 150 prospective tenants met my screening criteria. That means out of 150 people I only showed the place to 5 people. The rest were rejected since they did not meet my screening criteria.