I refused to use my cell at my regional and routinely used pay phones inside the terminal to call MX on write-ups if the gate's phone didn't work.
My Android phone has worked well on AA's FOS site, not sure what the guy above was referring to. Maybe he had an older phone.
I wouldn't base my phone decision on the use of company web sites, personally.
Cricket offers a good nationwide plan for $35/month using AT&T towers.