I am also researching this topic and all of the advice I have read so far is to treat your vetting of any MTR tenant the same as a long term/traditional tenant if you are not using a booking platform. Meaning, they will enter into a lease agreement with you that spells out the terms and conditions of their stay. I would perform a background check or have your property management site do that thru the application process. Keeping in mind that a lot of licensed professionals must go through a background check as part of the hiring processes. This is true for travel nurses, for example.
Now, if you're booking through a site like AirBnB the process outlined above may not be necessary. However, if you're using sites like Zillow or Furnished Finder to get leads on possible tenants then you will need to vet them on your own or through your PMS (property management software) and sign a lease. I ask for personal and professional references as well as any prior landlord references and the PMS I use includes a background check in the application process. Again if you're using a site like AirBnB or VRBO then you have the reviews from other hosts and some of the protections offered via the booking platform.
When I travel for work I bring certain kitchen necessities with me. It is so helpful to be able to cook meals in the place I am staying for weeks or months at a time.
Great wifi is also important!