I want to rent a car for a week and have been looking at a web site with cars from all the rental agencies. They list pickup at various hotels. Does this mean that one must take a shuttle to a hotel in order to pick up a car?

A bus from airport,will take you to the rental company office location. Bus service is every 5 mins and when you drop the car, you can bring your luggauge in the car and the take bus to airport.

You can take the bus or just an Uber or lyft that is faster

Everything you need is more close from you that you think !!!

You can easily uber or lyft when u arrive at mccarran. Or most major hotels have free shuttle bus pickups

Many rental companies have pickup available at the hotel, but there is also a rental center located at the airport (a very short/free shuttle ride from the terminal) that houses all the major car rental companies.