I keep mine in a special pin collectors bag. It has cloth "pages" like a book, where you pin the pins. This is the one I have, https://www.ebay.com/itm/Disney-parks-Accessory-Tinkerbell-Pin-Trading-Bag-/223512586992
I splurged and bought one from the parks- so they’re not on display but I really enjoy just flipping through it. My boys put theirs on a piece of cross stitch fabric, which they pin on the wall
I buy the plain canvas pictures from hobbycraft. I paint the background to suit e.g pink sparkly for Princesses, green and purple swirls for villains, red and gold for Christmas etc. I usually wait till I have the full set or collection then I pop the badges onto the canvas. There is space behind to keep the pin packs if I want to change display. They look great up on the wall in our study!
I use a bag that is very similar to this onehttps://www.shopdisney.com/mickey-mouse-pin-trading-bag-disney-parks-large-1445401
We have all ours on a cork board mounted on the wall. The board is sprayed black to enhance the pins