I did exactly this and it took me a while to work it out! Basically, you want to create a thing type “Amenity”. You’re also going to want to create an admin page for creating new "Amenity"s. Think of these objects as system globals that are only created by you or another administrator. They represent all of the different Amenities that one of your “Property” might have. Use your admin interface (you could also do this in Data > App Data but that interface is gonna be more clunky than what you could build yourself) to create them.
What you end up with is a list of "Amenity"s that just exists there in the database, each Amenity ready to be attached to other things.
Now, on your Property data type give it a new field. That field (which you could call “Amenities”) should be of type Amenity and it is going to be a List.
Your user interface for selecting what Amenity items apply to the Property in question can now just be a repeating list populated by “Do a Search for… Amenitys”. Put a checkbox (or your own sexier-looking checkbox type interface item in the cell). When the checkbox is toggled, add or remove the Amenity from the Property’s Amenities (which is a list of type Amenity)… Like so:
As you might imagine, Step 3 in this workflow is simply the case of doing Amenity List ADD if the Amenity is not already in the Property’s list of Amenitys.
I got quite a bit fancier with all of this and my own “Amenity” type actually has several list type fields on it (such as “Amenity Category” and “Amenity Options”). But this should get you started?
Best,
Keith