House showings and Tenant applications

Hi BP!

I have finally finished fixing up a rental and have listed it for rent. I have received much interest, and decided to just have an open house for a few hours to show the place to prospective tenants and collect applications, rather than trying to meet with individuals one by one (so I'm not driving across town everyday for a showing and dealing with people who are no longer interested, not qualified, or don't show up at all). I'm wondering the best way to handle applications and collection of application fees, as well as selecting the most qualified tenant. Note that this is a low income rental in a C-class neighborhood that is beginning to gentrify but still has a few years before it attracts very well qualified tenants. 

I have a pretty detailed application, so I'm hoping I can rank the applicants based on the application, and then verify information through a background check starting with the strongest. I won't know that until I collect all applications, and I won't have all applications until the 3 hour open house ends. 

I can collect fees and then try to return for those that I don't run a background check on, but this could be a hassle and I don't want to take people's money away from them for a period of time while they would need it to get another place if I don't choose them. Do I just take applications, rank them, and then call the most qualified, meet up with them to collect the application fee, and then run the background check? That seems like the best option, but just causes more work for me and the applicant to try to meet up again at a later date. 

Any recommendations on how best to handle? Thanks!