While we are driving our CAG Grace is in a small vari-kennel carrier, strapped onto the console of the truck. Once we are parked I've used folding dog crate for inside, along with a much bigger cage for outside. OMG we travel with three cages for one little bird :-0 We have a fifth wheel so I was able to remove one of the recliners to make room for her cage inside, so it is just a normal parrot cage.
Mess... well... I just sweep and clean a lot. When we are parked somewhere she spends much of her day in her giant outside cage so that keeps the mess inside under control. And we also plan out the menu i.e. no pomegranate inside!
(Btw - she is not a noisy bird, most people don't even know she's there).