There are several factors to keep in mind when designing or selecting a home (cage) for a chinchilla. These are outlined on this page.
The first consideration is the actual construction materials. Some woods and materials are toxic to chinchillas so you have to be very careful in what you select, because chinchillas DO chew. Some more, some less, but they are all going to chew regardless. Oak, manmade materials (MDF, Plywood, etc.), cedar and pressure treated are all unsafe for chins. Your best bet is poplar or kiln-dried pine. Do realize that some chinchillas will urinate somewhere other than the bottom of the cage and it will soak into wood. Most chins are very good about their "potty manners", but some are not. Any wood product that the chin would have access to needs to remain unfinished (no stain, paint, sealer or coating of any kind).
Any wire that is on the walls of the cage needs to be 1"x1" or smaller (preferably smaller), but the gauge of the wire needs to be thicker than chicken wire to avoid injury. We recommend 16 gauge or larger (the lower the number, the thicker the wire). Flooring (if you are planning a raised wire floor over a dropping pan) should be 1/2"x1/2" or smaller, and the gauge needs to be larger than 16. That's going to be hard to find as hardware cloth is a fine gauge. We have used 1/2"x1" with fairly good success, but the smaller the better. The roof can be whatever size (up to 1"x2"). The reason the walls have to be the smaller mesh size is because chinchillas will sometimes "bounce" off the walls with their hind feet. Larger mesh allows their feet to slip between the wires while they're in mid-air and broken legs are usually the result. We've have had it happen to a rescue in a donated cage, so we know this to be true. Building a safe cage is a lot cheaper and less hassle and upset than a chin with a broken leg!
The only plastic that is safe to be in a chinchilla's cage is PVC. Chinchillas can and do chew (as was mentioned before) and most plastics will break off in big hunks and can be swallowed. PVC doesn't do this and has very fine pieces so it's considered relatively safe. Any PVC pipe should be at least 4" diameter. Elbows and T's are ok, but avoid Y's. You could build things for out-of-cage playtime with black corrugated drain tubing, since the chin would need to be supervised while out of the cage anyway. In this case, it would be imperative to stop the chin from chewing on the plastic immediately. Whether or not a chin will use PVC tubes really depends on the chinchilla. We have tubes in a few of our cages (mostly in our own personal chin's cages, but a few rescue cages have them too). Some of our own chins and some rescues actually sleep in them (we have 6" pipe in the one that uses it the most for sleeping), some use them to run through to get from one place to another. Mount them completely horizontal, don't put them at an angle because chins probably wouldn't be able to get "up" a tube. We use a max of 12" sections, in case for some reason we have to "remove" a chin from them. We prefer the thicker PVC, personally, it holds up a little better. To mount the tube on the side of the cage, drill two holes in the side of it, placed so they line up with the center of the mesh in the wire, far enough apart to offer good support. Use round head short bolts from the inside, a washer big enough for the mesh of the cage and a wing nut for each hole. Just make sure the edges of the pipe are smooth (sand or file them after cutting), so the chin doesn't cut his or her little feet.
Size DOES matter! If you want something that looks more like furniture than a cage, remember that it will be somewhat permanent. If you think youll need to move the cage to a basement or elsewhere if it gets too warm for the chin, the weight and size is going to be a consideration. You're going to want a size that is comfortable for the chin, yet easy for you to move if necessary (you'll want it manageable for moving to clean around the cage anyway). The cage size we use most here for one or two chins, is 30"w x 18"d x 48"h. It's modeled after a cage that is available online. We've found that cages larger than 30x24x48 offer no real advantage and have a lot of wasted space in them.
If you go here, you'll see some links to companies that sell decent chinchilla cages and our opinions on the pro's and con's of each one. The photos below are Martin's Highrise's. The one on the left belongs to our Quinci, the one on the right is our Ananya's. Both of these cages were gutted (you can order the cage without the inside shelving) and outfitted with all wooden shelves. Note that Quinci's cage we used a full middle floor with a ledge below the opening in the floor on the right (you can just see Quinci on the shelf below the opening). Ananya's cage on the right, is outfitted differently and has an "L" shaped shelf that has the house secured in position (but removes easily for cleaning) so it cannot fall off and hurt her. The full shelves are a combination of 1x8's and 1x10's. The corner ledges as well as the full shelves add a lot of stability to the cage. Since the photo of Quinci's cage was taken, we reversed the full floor and made the entire cage a mirror image of what was. This moved the saucer away from the door, for easier access the lower level for cleaning and food replenishment.
Here is also a link to a plan you can download. We have not made this cage, but had planned to before we started the rescue. It is going to be very heavy (a permanent fixture), but we've read on one of the forums that we belong to that a lot of people have made them and are happy with them. It uses melamine covered MDF, which makes it good for cleaning (we still prefer wire), but we'd suggest making the shelving inside out of 1x pine instead of the melamine. They'll chew them, but they're cheap to replace, and chewing is good and necessary for their dental health.
If you plan to put a wheel in the cage (we recommend them highly....if you can't get the chin out to play and exercise, they have something to burn off the energy), it needs to be a safe one (examples of safe wheels). We recommend deciding what wheel you want and then planning the cage accordingly.
Ramps are not necessary for chinchillas and can sometimes be unsafe. Chinchillas like to hop from place to place, so we recommend just putting the ledges in strategic places. The exception would be if you put a full middle floor with a small access hole in it. If you put a ledge right under the hole, about 6"-7" below it (depending on the size of the chin), the chin will be able to hop up through it. The recommend hole size should be about 4-1/2" diameter or so, but at least 4".
Spacing of the shelves should be about 6"-8" in height from one to the next (a little more is ok, depending on the abilities of the individual chin), and jumps across no more than a foot to be safe. No place in the cage should there be a drop straight down of more than about 18" for safety.
We also highly recommend slide out pans of some sort. They are so much easier and faster to clean than the drop-in style (which means you have to lift the cage up and out of the pan.