First Rental - Could use some advice

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Hi Everyone,

Roughly over a year a go I purchased what would become my first rental/investment property. I used my VA loan to acquire the property, lived in the house (SFR) for a year as required, and now I am ready to turn it around and rent it to a tenant. I will not get into specifics in this post, but the end result of this transaction will be a cash flow producing investment once a tenant moves in. Really excited!....also a bit nervous!

The situation I am currently in is the following:

• I have multiple offers on the property. Some relative lower than what I want, another at asking, and the rest somewhere in between.
• The one at asking which is my preferred at the moment interviewed great; seemed like a very nice person. She informed me that her husband had recently passed away, and is therefore looking to move ASAP for a fresh start. She is local to the area and has been living in her current residence with her 4 kids for the last 11 years.
• After running her through SmartMove (thank you BP!), the results were not favorable and the system recommended a decline based on low income and 4 accounts under collection
• I then contacted the applicant and told her that we had declined her application for these very reasons, to which she responded that her income was over $100k/yr, enough to qualify, and that she had fallen into a rough patch and financial challenges in the 3 years leading up to her husband's passing due to pancreatic cancer. 
• She mentioned this was all on her, and that having to stay at home and take care of her husband had caused her to lose her job and so she fell behind on her obligations. She has since retained a new position.
• However, she mentioned that she never fell behind on rent, and that she can get a recommendation letter from her landlord, who she mentioned is willing to talk to me.
• She is currently repairing her credit, and mentioned she could up the security deposit if required

Based on all this, I want to say that we stick to our qualification criteria and decline the application, but I would be interested to hear from those here what your thoughts are on this situation.

Thank you very much for your support :).