Whenever I sell items, I usually ask for wishlist items to complete my catalogue, or a visit to Able Sisters shop. I also ask for rare crafting materials like gold nuggets or rusted parts if I have a rare/expensive item. Other times I'll do a 1:1 trade, for things like the Nook Mile variants. Bells are useless to me so I never ask for that. When I had a shop for New Leaf, I always sold for TBT but I haven't sold for TBT at all for New Horizons. Once I have literally everything in the game, I will probably switch to selling to TBT but for now, wishlist items to complete catalogue is my favourite currency to ask for!
As far as when I purchase, if the price is fair then I'll pay with whatever the person is asking for