One thing I like about Costco is that my wife is automatically covered when we rent a car through any of the companies.
Warning though concerning Budget and Costco. When I went to pick up my rental car from Budget at LAS, the price came up different and I didn't notice until they ran the card. I did manage to talk the agent back down to the original price by waving my printed confirmation, but the credit card account still showed the higher price. When I called Budget customer service, they said that they had been having problems with Costco rates not going into their system properly and that my card would be adjusted when I returned the car. (This did happen with no problems when I returned the car.)
Word of Warning - Make sure you have your Costco reservation printed and check the amount before you let them swipe your card.
I asked why their agents weren't aware of this glitch, but never got a good answer.