Just be aware of how “verification” works on Airbnb. I would be especially concerned if I had kids around.
From https://www.airbnb.com/help/article/1308/does-airbnb-perform-background-checks-on-members
Although background checks may help identify past criminal conduct where records are available, background checks don’t always identify a person’s past crimes or other red flags, they are never a guarantee that a person won’t break the law in the future. Due to the way certain databases are maintained, there may be gaps in the coverage provided by public records searches, and the online databases may be only updated periodically by local governments which we do not control or direct. Results of these database checks may not reveal or include include recent criminal record activity.
No background check should ever be relied upon as the sole indicator of suitability. You should always exercise your own judgment about whom to interact with and follow other sensible safety tips.
Also be aware of insurance. Make sure if you pay a mortgage that the bank that owns the loan is okay with it (try to find out indirectly) and find out what kind of insurance you need to do it.