I just became a new owner a few months ago so can give some insight. My cage I bought off Craigslist for 50$ but nice cages can cost anywhere from 50-100$ and up. Extra supplies including a water bottle, a food bin and hay holder, a hidey house, first batch of food, wood and toys was about another 100$. Depending on where you get your chin from, you may also want to consider getting a wheel (my boys were adopted and never showed interest in a wheel). Good wheels are also around 55 and up. Basically what I did was prepared for my chinchillas slowly over 2 months. Set up the cage and it's accessories which included a hiding house, a hammock and a soft house. The fleece items I made myself but online they cost average 10-15$. After I knew exactly when I was getting my chinchillas, I went on a pet store shopping spree. Buying alfalfa cubes, hay, chewing sticks, the hiding house, food holder, water bottle, tubes etc. which like I said before, depending how much you are willing to spend, may cost upwards of 100$. Finally after I got my chins, even though they had plenty I ordered healthy treats, chews and pumice for them for around 30$.
Now I actually ended up adopting my chins for free. But since I did a lot of research, I can tell you average prices. From rescues and classifieds, they are usually around 50-75$. In pet stores they are usually priced at 150$ but are usually always only standard grays. From breeders, they will sell older chins but the lowest price seems to be 100$. The ones that are in better shape or are show worry are usually 150-200$ but usually not more than that. On average, to get started. As an over estimate I can imagine counting around 100-150$ for the cage (usually from online, eBay amazon) depending how elaborate you want them to be, can come over 200$. For the first amount of supplies and cage accessories, probably 100$-150$ also depending if you get the wheel which is probably one of the most expensive items for chins. The chin itself will most likely be on average between 100-200$ unless you adopt. Basically I would have to say you can be spending anywhere from 300-500$.
People might disagree with me but I would try and find used cages and definitely adopt if you're up to it.