If you really want to see Paphos and the surrounding area, it will be very difficult without a car, because buses run infrequently and many picturesque places are simply inaccessible. I usually use car aggregators, such as https://findycar.com/car-rental-paphos/ , where the keyword is "Car Rental Paphos." On the website, you can compare prices from different companies, choose the car class you need, and check the insurance and deposit conditions. For a family vacation, it is better to choose a comfortable car with air conditioning and a large trunk so that all your belongings and beach equipment will fit. You can also book a car online in advance to avoid queues at the airport and higher seasonal prices.