1. What are you planning to do? Your original post seems to differentiate yourself from the cardboard box crowd that tours. As noted, you can travel and tour with a plastic case if you will be doing a supported trip that carries/stores the box or an unsupported loop. I have done both in Europe. For the loop, I started and ended at a campground that was willing to store my box for me without charge.
2. As noted, carboard boxes work fine if the box is properly boxed. Remember that there is a halfway decent chance that your bike travelled from a far away land to you or your local bike shop in a cardboard box via boat and then via truck and possibly even train as well.
3. If you are looking for an plastic case, CrateWorks makes a large, "semi-hard" case that's not as expensive as many hardcases. Despite its size, it is still under the max dimensions allowed by airlines such as Southwest. Saw lots of people using them on Cycle Oregon this year.