@Rhiannon Then You can click on Tools and Tenant Screening to be taken to the TransUnion site.
I think you should use the property manager. It sounds like they have the experience to know that marketing the best $700 rental in town will get you the best $700 renter in town or someone who can afford more, but lives within their means. This is how you get low headache tenants.
I disagree with your assertion that you "know your neighbor." Tenants who claim "mold" or "lack of repairs" and then they're living in their Grandmother's winter house are likely problem complainers whose only real grievance is that they do not have their rent on time or, eventually, at all. I note that Grandma does not like the arrangement - either she really intends to sell or she just wants her Grandaughter to become your problem instead of hers, but we do know for sure this lady's own Grandmother doesn't want her as a tenant. My vote is with Grandma.