You have two options when it comes to cages for chinchillas. You can build your own or you can buy one ready-made. We've actually done both.
Our first cage was typical of pet store cages. Its dimensions measured 3 feet x 1.5 feet x 2 feet and it had two levels. It seemed to be a decent size for one chinchilla, but it didn't take long before we started to think about coming up with our own design. The main advantage of a store bought cage is immediate availability. Pre-built cages can also be reasonably priced given the economies of scale inherent in mass produced products.
Our second cage was one we designed and built. We wanted to build something as large as possible, but still be small enough to move around our house as needed. This meant the cage had to be no wider than 2 feet so that it could fit through a doorway. The length was determined by figuring out what we could maneuver around the hallways of our home. This turned out to be 4 feet. And the height was also 4' mostly because of the size of the materials that we selected (more about that below).
The custom chinchilla cage we built has a 5-sided base (i.e. 4 walls and a bottom) made out of melamine. Melamine is particle board covered with white plastic that is easy to clean with Windex and a paper towel. To make moving the cage easy, we attached strong caster wheels to the bottom of each of the 4 corners.
The sides and top of the cage are made out of white Elfa shelving you can buy from the Container Store. Holding the whole thing together are 1-inch square pieces of wood that run length-wise or width-wise throughout the cage. These pieces of wood also provide support for wooden shelves (4 levels) that the chinchillas can jump onto. The Elfa walls and ceiling form another 5-sided box that sits within the melamine base. Both the melamine bottom and Elfa have a door to allow for entry to and exit from the cage.
To make the cage easier to clean, we put together a 5-sided wooden box which we filled with bedding as a cue to our chinchillas. The wooden box also has a melamine bottom, but it has pine sides since they're exposed and may be chewed.