One thing to expect at PHX is that the "rental car facility" is offsite and quite some distance from the airport. Driving from/to it is somewhat confusing (there are some tricks to avoid traffic). Allow extra time for this step. The last time I was there (about nine months ago), I experienced some bad road construction around the terminal and also near the rental car place, but there's a chance that it's finished by now.

Moreover, expect a lot of traffic and aggressive drivers on the expressways around Phoenix. Personally, I wouldn't want to try to drive here (on the wrong side of the road for you?) after a long TATL flight. Stay in an airport hotel (or go to Tempe/Phoenix/Scottsdale for a pleasant evening) and return to the airport the next day to get your rental car.