First rental and screening. How to proceed?

[Dean C.]

My wife and I are looking to rent out our first property. We've been advertising for about 2 weeks and  after screening out several who were obvious they wouldn't be a good match for us for various reasons (bad credit, don't earn enough income, don't want a 12 month lease, etc.) we have our first prospects that look like potential tenants (husband, wife, 2 young children).  They pass all of our minimum requirements except income.  

Their monthly income is only about 2X monthly rent but husband was injured last year on the job and was granted a workman's comp settlement and as such is sitting on a pile of cash. He led us to believe it was enough money to live on for a few years while he completes his engineering degree. Before I knew of all this and I discovered his income was low during the pre-screening process, I informed him this wouldn't be a good match. That's when he informed me of his accident and current cash situation and offered to pay last 6 mos. rent along with deposit and such.  Their other bills look good so I'm wondering what the good folks at BP would suggest? We showed them the property and they seem like a great young family. I was thinking about proceeding with the application, verify his cash situation via recent bank statement, etc.  Would you go so far as having him get a guarantor (cosigner) for rent? Any other suggestions?  Thanks in advance for any help!