There are many bedding options out there, but not all are appropriate for chinchillas. For example, pine shavings are generally considered safe for animals, but not so for chinchillas. Some pine shavings can contain a resin that when ingested will harm a chinchilla.
The best option we've found are aspen shavings. These shavings provide the same benefit as pine, come in bulk so the price is low, and are not harmful to chinchillas in any form. We've also tried a recycled paper bedding. This product appealed to us because it was recycled material and very absorbent. However, on too many occasions we saw our chins eating the paper which raised concerns that there may be digestive issues down the road.
Our chinchillas are pretty good about using their bedding rather than urinating outside their cage.
Your nose will tell you when it is time to change the bedding. The frequency will also depend on how much bedding you provide and in how large an area. In the interest of easy cleaning, we use a relatively small bedding box that is about 1' x 2'.