Advice needed on whether or not to rent to someone!

[Dianna Marble]

I could use some advice on a potential tenant for our rental unit. I am going back and forth on whether or not to lease to them. A couple came to look through the unit and wanted to submit the applications to lease it. I received the application that only the wife filled out, even though I gave them 2 applications so that we can run credit and background checks on both tenants. The application I received was filled out but, not in full. She didn't fill out a few areas including her current landlord's phone number. The husband warned us that his credit is not great because of past medical bills. I let them know that I would need the husband to fill out the application as well and he did and sent it to me right away. I then asked for proof of income, which ended up being slightly different than what he indicated his income was on the application. On top of that, during walking through the unit, they told me that they had the security deposit and first month's rent available immediately but, I happened to check out the wife's facebook page and she had set up a GoFundMe page to help with the deposit and moving. The GFM page said that they haven't been able to save any money because he husband wasn't working. I ended up asking about the GFM page and she said it was an old one she made last year that just happened to update. (Keep in mind that the page said it was created 2 days prior and was specific on when they had to move.)  Also, the husband is working but for a temp staffing agency. So, lots of red flags for me. I am wondering, am I being too cautious? Am I overthinking things? I seriously HATE being lied to. I don't want to jeopardize our investment but I know there is no perfect renter out there. With this situation, would you rent to these people? 
***Please be kind with your responses. I am new to this business and still learning. Thanks!***