When I raised my baby chicks (purchased as hatchlings) last spring, I used a Rubbermaid type plastic container with a lid. I used a clamp-on utility lamp with the metal reflector on it. I put a short two by four board across the container and clamped the lamp to it. The board also kept the container lid propped open a bit to allow for air exchange. I used newspaper covered with paper towels on the bottom in the beginning. Then I switched to aspen pet bedding once the chicks could tell the difference between food and bedding. Whatever container you choose, I would recommend that you get one taller than you think you might need. After only a few weeks, my baby chicks were hopping on top of the waterer and trying to figure out how to hop out of the box.
I have two curious, older, indoor-only cats who looked, but never touched my baby chicks. However, as you know, your mileage may vary depending on your cat's behavior. From my childhood, I vividly remember my pet tom cat. He would find fledgling baby birds on the ground in the spring/summer and run under a car or trailer where I couldn't reach him to enjoy his meal. I used to agonize over the slaughter of the baby birds. So now, I keep my cats indoors where they aren't a threat to the local songbirds. Even with my docile indoor-only cats, I still don't trust them when it comes to animals their size or smaller. Every once in a while I find my cats with a small, live lizard in their mouth which has somehow wondered in from outdoors.