I usually fly over to the GD at Warhammer Fest in May, so i'm always conscious of transporting models and the size I can manage on the plane.

Usually my models base is incorporated into the base provided with the model, and I've a small carriage clock box that has some really soft foam I use to secure it in place for the journey.

In terms of plinths I think it does help grab your initial attention but you don't want it overpowering the model. If the model and base only sit on the plinth I'd advise magnetising or at least blue-tac it to the plinth - the judges might not realise it's not secured and then whoops, there goes all your hard work!