Since I have eggs hatching almost every week, I have different set ups. The first is just a small bird cage from the store. I does keep the cats and dog from getting the chicks. I have a heat lamp clamped to a book shelf to heat the cage. After the chicks are eating and drinking and moving around, the they can go to the other set up. This is just a pen from the farm store. I have a radiator heater. This is so they can get sleep at night. I also cover it with some old plastic lattice material from Lowe's. This keeps them from getting out and animals getting in. Basic caging screen would work the same.
After about a month old, they can go outside to the box. This is just a, old chicken coop I've put on the ground (removed the legs) and taken off the top part (shortened it). In short, I disassembled and put together my way with modifications. It keeps them warm and protected from the weather. The box was put to the test last week with a surprise May snow. It also has a lid and side door. I kept the door closed and moved the food an water inside the box. All the chicks survived outside in the box.
The box can be moved around. Inside I have a radiator heater set low, so the smaller chicks can get under while the older ones can not. The older ones are fully feathered. Currently I have it set up inside a dog pen that has been modified with chicken wire and mesh. The chicks can not get out of the dog pen and with chicken wire covering the top, the cats can not get in.
I have another outside cage where the box completes one side. With this the box keeps them warm and they can have access to the dirt and sunshine. This cage is just a from of 2x2 and chicken wire. So other animals can not get to the chicks.
I make my own cages, and have made most boxes and cages for farms. So it should be easy for anyone to build their own suited for themselves. I don't see the need to go buy some fancy cage from the store unless you just don't have the time.