I think that's it. Did you see any 不良 public record in the credit report, except mortgage late payment because you know they go for short sale already, like other bill (credit card, medical, utility) late payment?
You can ask two months deposit. If they can't come out that, then negotiate with them for 1.5 months. And put lease term a little bit tight. Like rent due is on the 1st day of the month. If not receive by 3rd day 5 pm, charge $50 late fee per day; If not receive by 5th day 5 pm, start eviction etc.
Get their personal information as much as possible. SSN, CDL, Bank account, cars' plate #, all cell#, home phone # (when they move in), both work phone#, e-mail address etc.
Don't forget to put it in lease form: Can't bring the truck into property site.
Do some more study to get a really good lease form.
Good luck!