Is it possible to remove the wire floor? I know some cages it's a wire grating that can be removed. I doubt putting shavings on the wire would be a good idea at all, it wouldn't protect the chin from the wire and would make a huge mess. You want to make sure the chin can't get it's toes or, if the wire is wide enough, legs caught and broken. Another option would be to get a metal pan to fit the bottom of the cage.
Bass Equipment sells different size pans, and they can custom make them too, unless the cage floor is bigger then 48"x30" in which case I would just get two pans.
As for fleece, vacuum all the poop, hay and other stuff off it, then you wash it in the washing machine with about a cup of vinegar for cleaner. Depending on how much your chin pees, and how sensitive you are to the smell, you will need to change out the fleece a couple times a week. I recommend also getting a shop vac for cage cleaning, otherwise the vacuum just keeps getting clogged with the hay and sticks. The upkeep is basically the cost of washing it. The most expensive part (unless you pay for laundry) is buying the fleece. If you can make your own liners it's the cost thread and the fleece, which ranges depending on designs you want, so anywhere from less then $10 a yard for basic solid colored to over $20 for licensed prints (Disney, sports teams, video game or cartoon character, stuff like that). You want the fleece to be at least 3 layers thick to absorb pee, I prefer using fleece in the middle, but other people use batting or towels. If you are having to buy the fleece liners, it depends on the size and how many you need, probably around $20+ for one floor liner (it varies from vendor to vendor and on thickness you want). You will also need at least 2, so you can put a new liner down while washing the other.
One other thing to keep in mind though, although most chins don't chew fleece, some do. If your chin chews the fleece you will need to find a different bedding to use. Fleece is only safe if the chin doesn't chew it, it doesn't shred like other fabric, but it's still not digestible. If a little is swallowed before you notice it will likely pass without a problem but if a lot is swallowed it could cause a blockage.