I magnetise my models and movement trays. That's usually enough to cope with anything short of a big speedbump during transit. At the moment I'm just using battalion boxes to transport my models, relying on the magnets to hold, and the models to be heavy enough not to bounce. I want to magetise my movement trays to the actual boxes, but :effort:
I keep all my terrain in 2 stackable plastic boxes. They do get a fair bit of damage done to them, mainly when putting everything back in, though that's just because we're not careful enough. I think a big part of building terrain is designing for your storage/transport methods. Know your box size, and how it'll all fit in.