First and foremost you need a good company that does good background checks for a reasonable price. There is a company that tell you a lot about someone, www.BeenVerified.com. Now they don't run background checks, but can verify the person is who they say they are.
To allow certain people to view the property in your absence, there are locks now that use Bluetooth to unlock them. You can actually text them a code that will expire in a short period of time. They don't know the code so they can't hack it later. There are actually locks that you can add to a bolt action already on the door. It simply unlocks or locks the door by actuating the bold lever.
You can also purchase a wifi hot spot from a cell phone company and use Ring or another security camera to actually view them while they are in the property. I'm sure you've seen some of the ads on TV that have the owner remotely talking to an intruder. You can talk to the prospective tenant while they are viewing the premises and actually view some of their friends they bring along. You can also add wifi lights and thermostat, allowing you to control the lights and temperature at a distance.
Only allow them to enter the premises in your absence after they email you a photo of their driver's license and if it is more than one person, get photos of all of their driver's licenses.
After renting to them remove the remote entry wifi lock and put on a Schlage or Honeywell keyless entry lock. These locks are not remotely controllable. Now they come with keys, just don't give the tenant the key. These are programmable combination locks and you can find them on Amazon or even at Home Depot or Lowe's. Build.com sometimes have refurbished ones with a full warranty at greatly reduced prices. The prices run as low as $75 ea. for refurbs to $129 at Home Depot/Lowe's. They allow you to program them with a combination specific to that premises. I usually use the tenant's birthday. If it is a couple I use her birthday, she'll remember it, and he better had. LOL
Only put a single combo on it for them. You can add up to 20 others though. You can add a throw away combo for a repair man. You can discard these after used. I also add a combo specifically for me and it is on all my locks. That way I don't need to know the tenant's combo to enter the premises if I need to. In addition, you can change the master code, I call it the God code. All my locks have the same master code so when needed I can clear any of the locks of all entry codes.
I use these locks on all my units. They are great and have a life time warranty. The only time I ever had trouble with one, Schlage replaced it free of charge.