I’m planning to build one at my next house (fingers crossed), and my current plant is similar to what js mentioned. Chain link fence for strength against large predators. I plan to put either flagstone or concrete as a barrier at the bottom of the perimeter to prevent digging. Then I was planning to put small diameter metal (not plastic) mesh fencing to reinforce that to keep birds and other small creatures out. My plan was too do this everywhere, not just lower down. I’m avoiding cheaper plastic mesh because it is often just big enough for small snakes to push into and then get stuck midway through, and I don’t want to have to cut snakes out of the mesh. For the top - something strong enough and visible enough to keep predators from scaling it and getting in and to discourage birds of prey from doing something foolish, once more reinforced by the small metal mesh to keep smaller things out. This spot is for cats only!
I’ve seen enough chickens killed by raccoons reaching through large diameter fencing to want to prevent anything from being able to reach through and I want the cats to experience the great outdoors, not to have the smaller creatures of the great outdoors end up trapped inside with them and brought into the house half dead.