In my experience the basics for a functional RE based CRM are:Custom Fields for Data Objects (Leads, Prospects, Applications, Buildings, Units, etc...)A Screening Engine (background/credit checks, employment verification, etc)Online Rental Application (this should automatically run the application through screening)Ability to mass email/sms leads and tenants to provide informationSurveys/Inspection formsI've been building real estate CRM tools for years.

And lenders are at end of day just statistics machines, that is the job of an underwriter, to quantify an applicant into a mathematical risk score. 

In this case their total household income (of the husband and adult son combined) does meet the requirement of being 3x the rent, but how should I apply requirements of good credit for this and other applications with multiple tenants in one application? 

Unfortunately, I have not had much success as I have barely gotten 1 application.

I used Zillow to list my rental and accepted someone's application however after my few interactions with them on the phone some major red flags have come up and I wanted to know am I under any legal obligation to rent my property to this person. 

However, there may be alternative tax strategies out there that are more applicable to your current situation or property.

Perform the same task in each app to ensure a fair comparison.Load a property with pictures and details.Market that property.See what your marketing looks like from the public's perspective.Submit a fake application to see how easy the process is.Run a credit/screening report on yourself.Enter a maintenance request, assign a vendor, and attach a fake invoice.Enter charges to the tenant's ledger.Enter recurring charges and automatic late fees.Sign documents electronically.Run owner reports.After testing a few apps, one should clearly stand out.

No test, no experience, nothing else needed (beyond an insurance policy number to complete application).  

@Demetrius Lindsey yes, this is still applicable today.  

It's nice to meet them in person before screening their application.