@Courtney Downtain
I would never let a tenant in by themselves. Last thing you want is a squatter that you end up having to evict after they destroy your place.
I agree with @Mike Dorneman & @Matthew Paul I also do the prescreen telephone interview and only setup a showing when they meet the prescreen criteria of adequate income, no prior evictions, referrals, no smokers and no pets (in my case). I then set a couple hour window for showings and scheduling a window for each tenant. It seems to work pretty good. As Matt said, you get to see their car and how they are dressed. Often times, the inside of their car is a reflection of how they would keep the inside of your unit. However, I have had situations where they were driving high dollar cars, they were dressed to the hilt yet their income barely made my minimum requirement (3x rent). This to me indicated that they probably had other priorities with their money and as Mike said, paying you probably won't be a priority.