Cardboard is way too heavy and too flimsy to build a good airplane.
Have a look at https://www.flitetest.com/articles/t...nner-ft-planes and pick one of those if you want to build something. The experimentation has already been done on them, so you will have a reasonable chance of success. You won't save money by building, at least not for your first project. Learning to build can save you money in the long run though as you will also learn to do repairs and can transfer components into new projects.

Cheaper and easier would be to buy a ready to fly model like the Hobby King Bixler.