I didn't replace my kitchenaid mixer, but I did give away my bread maker. Also wood, plastic colanders, baking pans, anything that stuff would get crusty on. I kept all my glass cookware though because when I clean something, no spots are acceptable. If you are the kind of person that leaves baked on stuff on cookware, things of that nature I would replace. Since you said you got your KA mixer recently, I would assume it hasn't had time to get really grimy and crusty so you should be able to clean it with confidence. I also took the chance to re-prganize my pantry and cabinets and wiped them all down really well because of crumbs and such.
If you have an expensive appliance that you think you need to replace, you can probably sell it on craigslist to help offset the cost of a new one. For my birthday after my diagnosis, a few family gave me gift cards because they knew I would have to replace a bunch of things, also with Christmas coming up, don't be ashamed to spread the word about your need for kitchen items