What would be the cheapest (and easiest) way to get from IAH to AUS?

Hi everyone. I'm traveling from Mexico City to Houston via airplane and must get to Austin (preferably near the AUS airport). What would be the cheapest and (preferably) easiest way to do that?

My first thought was to take a bus, but it seems complicated (get out of IAH and go to downtown Houston); so, I was thinking a car rental? does anyone know what the car expenses might be? and how much do the rental companies block on your card?

I hope you can help me. The trip is for March 1st. Thanks in advance, everyone.