It all comes down to how many different species you'll be putting up fur for, how much resources you have to make your own gear, and to what end purpose you will be preparing the fur. You'll need at the very least a fleshing beam, stretcher racks, a good selection of knives and fleshers, a production area, and storage space. If you're doing yotes or other larger animals, you're probably also going to want a way to hang them for skinning because it makes it a LOT easier; it's also easier for small animals, but not quite as imperative. Finishing materials and consumables (brushes, sawdust, tail tools, various powders, soaps, flea/tick treatments, washing tubs and buckets, drop sheets, etc.) vary depending on your location, working area, and the season.
If you have a wood shop, you can make the majority of the supplies you will need yourself very cheaply. If you are putting up furs for personal use and do not plan to case them, you don't even need to make stretchers. During the winter I stretch on peg board in my basement, and during warmer weather I rack out on an old chain-link dog kennel in my back yard, but I don't sell my furs. But if you're sending off to auction and have established that you are capable of a consistent take, you're going to want to have a good selection of stretchers on hand because each fur is likely to be on them for several days. The rest of it is really up to what you find works for you in your space and what you are working with . . . you're going to need a lot more soap, peroxide, and wash bins for example if you are putting up ten skunk a week as compared to a couple of yotes a month. So that sort of thing is answers only you know.