You don't actually need much "new" stuff at first, depending on what sort of cookware you have, already. I already had and used mostly the old fashioned stainless steel pots/pans, so they were okay. It is the porous stuff you have to worry about. For example, we had an ancient toaster oven with a metal wire rack, until I replaced it, that rack got scrubbed, the crumb tray scrubbed, and then it got foil on it. I still use a newer toaster oven, because the rack is cleanable in case there is a cross contamination "oops" (and there has been, I had to switch flours several times). If you really want toast without a toaster, you can just broil something, watching it carefully. Cast iron is porous, it will need to be really, really cleaned, the old finish can get burnt off in the oven, and then scrubbed and a new seasoning (oil and heat) done to it. Seasoned cast iron should never be cleaned with soap, once it is seasoned. I clean mine with baking soda, vinegar, and water and wipe it out well and rinse it and dry, A cutting board - porous- just replace it, period. Wooden spoons- no. Replace or just don't use them, put them in the "donate" box. Ditto rubber spatulas, replace when you can, in the meantime, just don't use. Colander: not worth it, not expensive at a discount store, just replace it now. (Since we wash so much fruit/veg here, I have a lot of colanders... in different sizes ) Wooden rolling pin: use a drinking glass instead, and roll out your dough between 2 sheets of waxed paper. Ceramic and glass baking dishes are okay if they are just cleaned thoroughly.
Storage tupperware: porous. Don't use, replace at will. So many things nowadays come in tubs that you may find yourself just saving the plastic tubs that safe food comes in anyway, like big tubs of yogurt or Cool Whip, for instance, and using those for food storage.
Teflon: ugh. porous. replace at will. You don't really need more than one fry/saute pan in this, and it would be easy to pick up at a discount, if you use that sort of thing. I had a lot of teflon bakeware, and regular bakeware, that had sharp corners, and years of burnt on grundge in the cracks, so I did replace some of it or ask for it for holiday presents. Then I found out I had a cross contamination thing going, so I had to stop using it. At least I didn't go hog wild on the replacements. What I did splurge on was some really nice ceramic ware recently, because that stuff is very cleanable and it works with what I was doing, and it is microwavable. The store had it on sale..... there I went.
Plastic measuring cups and plastic measuring spoons: porous. This is sort of obvious, so if you are a scratch cook, these things need to go, pronto, and get replaced with metal and/or glass.
My mixing bowls were already stainless steel and ceramic/glassware, so they were fine. The electric mixer - ugh. Look at all that caked on old flour grundge. Buh- bye. I bought another one eventually, but haven't used it as I end up just hand mixing everything anyway, and I have a small counter.
Blender: Gluten free dedicated, especially if container is plastic and not glass. I use a blender a lot to do things it was not exactly intended for, like grinding nuts to make inexpensive almond meal. Does rubber touch the food ? May want to replace at will. I am going to make mine another gasket soon out of a plastic lid to a tub.
Coffee grinder: see "blender." Also used to grind gluten free things, like buckwheat kernels.
Drinking glasses: if you have plastic ones, you may want to make sure you just use the glass ones for your beverages.
To- go mug for car: what is it lined with ? Might have to replace, depending on what you've put in it before.