I built one last year. It was a 4x4 brooder, 23 inches tall with 2 light fixtures hooked to a dimmer switch (to vary the temp) with a long cord that plugs into the wall. Looking back I would have probably designed it a little differently and not made it square (you have to turn it on it's side to get it through a door). You could use 2x2 furring strips for the frame and just cut the plywood to fit the frame. You can also use the 2x2's to frame the top and use the poultry wire to cover that frame. You can hinge the top or just build it to be pulled off. Hope I didn't confuse you too much. Last year was our first year to raise chicks and they seemed to like running around in there.
I used cardboard boxes for years as brooders. A large appliance box works great and can be found for free. I notch the top edges to fit a board across the corner or center and duct tape it firmly to hold the clamp on metal reflector shop light. I've used 75 to 100 watt white bulbs. I actually reused one big cardboard box for several years by duct taping a paper feed sack in the bottom which was replaced each brood.