I've found Blender to be fairly easy to use and fairly powerful, it's FREE and you can download it here
There are also plenty of willing helpers on YouTube who have created some great tutorials. Here are a few I used to help me build my first cup.
How to use Blender by +dillongo2
Two Part Blender Tutorial for Beginners by +tutor4u
Here's the cup I built/designed...
The reason I made the models was because I wanted to have a few more things we'd created in to view in Google Cardboard.
I'm really looking forward to sharing this process with the students, as they're keen to create more of their own content. Perhaps we could look at lunchbox designs next term as part of our focus on health and the environment.
It took me a little while to figure out how to actually view these using cardboard but I think I've got an app that'll do it reasonably - 3d model viewer it means the .obj files (you can export your blender files to this file type) need to be on your phone though in the 3Dmodels directory.
This is a bit of a pain, hopefully Google will help developers to create links to google drive files instead of having to download all the files to your phone. Once they're on there though it's just a case of opening the app and finding the model, dumping your phone into cardboard and enjoying :). I'd love to find a quicker more streamlined version of this so if you've got any ideas please let me know.