Well you should find the GPU and Cooler relatively easy to reinstall if you needed to remove them due to the weight of the heat sinks the mobo is usually pretty secure being screwed down, screws can loosen due to vibration but if you transport it in a box with packaging that will absorb some of it so yeah, simply reinstall any parts that you thought advisable to remove, the gpu and cooler, and plug the fans back into the fan headers, could give the power plugs a look over to ensure they're all seated firmly, then the pc should simply post normally all being well.
The system won't have to reinstall any drivers or software, it's off when you remove the cooler and gpu, stays off in transport, off when you reinstall them so it doesn't know anything has changed it will boot as before.
I always keep my original PC case tower box and packaging for transportation, there's nothing like those polystyrene fillers to keep it from wobbling around.