This caught my eye because we are also flying into Vegas and then going to Zion and Bryce.

Number one rule is to ALWAYS book the day before. Not just no cars, but what if your flights get cancelled, and you have to arrive a day later. We're just staying our first night in Vegas at a hotel near the airport, but it gives me the assurance that even if something happens that first day/night, we'll be able to head to Zion the next day. I have much coveted reservations both at the Zion Lodge and also the Lodge at Bryce Canyon. It was not easy procuring those, and barring something truly unforeseen, I would not want to mess them up.

Same if you are arriving anywhere to go to a Show, a sporting event, whatever, just have that extra cushion.

And in terms of car rentals in general, I shy away from the cheapest (Fox, etc.) and the most expensive (Hertz, Avis). My sweet spot is Alamo. They have treated me very well.