I don't like having to shuttle to an off-site rental car facility but McCarran will hook you up. First of all, don't be scared of renting a car in Vegas. Valet parking is free at pretty much every hotel on the strip. Just tip em a couple bucks. $5 if you're feeling generous.
If you rent a car, walk outside to the 2nd curb and a rental car bus will drive by every few minutes. The driver will help load and unload all baggage. Nice. The lines have never been too long at McCarran and you will meet someone outside who will walk you around your car. It's easy getting back to drop off your car and can always do early bird drop off if you need to fly early.
This is better than standing in line at the airport for the mass shuttle to the strip for $7 or whatever they charge you on the spot and then trying to ignore their sales pitch. You have to stop at every hotel on the way to your hotel. You also won't need to wait for the return shuttle when you fly out. Or if you plan on drinking the whole trip and don't need to drive then just cab it to and from the strip- worth it to me.