I would just take an UberX. They're always on the ball, lots of drivers around here no matter what time of day/night. I have maybe taken 10 rides tops, so I'm not super expierenced, but every single time has been great.

I take it you'll be at sky harbor? Looks like an UberX would be $9 to $12 as of right now (no surge). ~5.2 miles. http://uberestimate.com/fare/cyvfwzh/

Enjoy your stay! Just starting to get warm