You'll be able to find a motor that fits your specifications on
www.globalspec.com.
As for size of the motor and how much power will be required, I would look into how high you're looking to lift the patient/gurney. By doing this, you can calculate the required potential energy change which can give you an idea on battery sizing.
Also I have to ask- why the heck would you want to carry a patient up stairs on a gurney? What about elevators?