By most city laws, you must take a stray cat to the shelter. You can ask for 'first rights' if you want, giving you the opportunity to adopt the cat first if the owner does not claim the cat. Some shelters now have a lost and found listing in the lobby if you decide not enter the cat into the shelter. Because cats tend to roam and come home days later, owners often delay checking the shelters, resulting in their cat being killed.
Cats do tend to travel.
The description should be vague, requiring more information from the caller. Require a photo ID of the animal from any caller, or a past veterinary bill. If you feel uncomfortable about having anyone come to your home, ask a local pet store if you can meet the other party there.