Renting to a family with under 600 credit

[Lallu Tappu]

Hi, I bought my first rental property and I am very new to the landlording scene so I'm hoping someone can help me with a conundrum I'm in right now. Since I was a little late getting in the property, I missed the summer peak and there is not a lot of people looking for a rental property now that school has already started. A beautiful family of 2 adults and 3 kids recently liked my house and are willing to rent it out. They told me upfront that they had poor credit due to medical bills and the husband had a felony charge back in 2009. I ran their credit and the same came up, however, no evictions and good job history. They lived in an apartment complex before who did not give out any information when I called them and they are currently living with family and are looking for a bigger place of their own. It all looks good but I'm not sure if I am falling for a sob story. What are somethings I should look for or do to make sure they really are trying to rebuild their life and not showing me a rosy picture. They do claim they are making all the payments on time and trying to build their credit back up so they can buy a house some day.