The cages I've been around all used 1/2" square hardware cloth for the flooring and standard "chicken wire" for the walls.
When I built one, I made the mistake of making the floor out of vertical 2x4's and attaching the legs to the outside of that frame. That created a 1-1/2" wide "rim" around the inside of the cage where the bedding, ***** matter and urine would collect. This caused issues with rust of the hardware cloth and rot of the 2x4's over time.
If I had it to do over, I'd put the legs inside the frame, or co-linear with the edge of the frame to avoid this.
Here's how I'd do it now - hope the description works without pics.
You can't really make this out of pressure-treated lumber - it will eat the hardware cloth and chicken wire.
Because of the size, you'll need cross-span supports to keep the hardware cloth from sagging and to allow you to tension it properly. I'd make those out of 2x4's, but I'd use my saw to bevel the edge of the 2x to narrow it down to about 1/2" wide.
Buy the hardware cloth 7" longer than the 72" length of the hutch. (79"), and 7" wider (if you can get it wider than 48"). If not, consider making the hutch 46 or so wide.
Make the frame and attach the hardware cloth across the narrow edge by tacking it to the end of the 2x4, wrapping it up over the top. Use 3/4" or 1" long galvanized U-staples - same stuff used for barbed-wire fence construction. Put the staples about every 4 inches.
Roll the cloth out and lay it over the frame. Take another 2x4 and lay it on the flat where it is almost falling off the end opposite the end you just stapled. Take another 2x4 and screw it to the top of the one below, creating a clamp on the hardware cloth.
Now rotate the 2x4/hardware cloth sandwich to allow the leading edge of the lower 2x to drop off the end of the frame. Press down lightly on the 2x and that will stretch the hardware cloth nicely. Put several staples along the top edge of the 2x, then release the clamp by unscrewing the 2x's. Fold the remainder over the end of the frame and staple the same way as the other end.
Fold the long edges of the hardware cloth over and staple the same way as the short ends - maybe stretch it a little, but I'll bet you won't need to.
For the sides, make them out of 2x4 stock, laid flat - don't worry about the legs yet. Make the ends 24" tall and 45" wide (assuming a 48" wide hutch). Make the front & back 24" tall and 60" wide. Put a vertical brace in the middle of the front & back.
Make them square or rectangular. Don't worry about roof pitch.
Use screws - pilot drill if you don't have screws with a self-drilling tip. Toenail the sides together and attach the chicken wire in the same manner as the hardware cloth. You can use smaller staples here, and it doesn't need to be stretched as much - it won't take much stretching without deforming.
Put two frames, short sides together, with a 2x4 loose between them on the floor (flat) and elevate the outside ends by placing a 2x4 under the end. Staple the chicken wire to one short end, and pull it across to the other short end and staple that end in place - wrap around the ends of the 2x4s and staple on the narrow edge.
Now remove the 2x4's and allow the frames to sit flat on the floor. Put some staples on the face of the ends of each frame, then remove the spacer 2x4 and cut the chicken wire, wrapping it around the end of the frames and stapling it there.
For doors, work those structures into the shape of the sides. It's a good idea to have the "house" for protection from the elements and for sleep, but make it a separate removable structure - makes it easier to clean the hutch and the house.
Screw the sides/ends together. The ends go between the front & back. Set the base on the walls, with the hardware cloth to the inside (facing down).
Cut 4 2x4's 40" long. Screw each 2x4 to the ends. This will hold the base to the walls when you turn the hutch over.
For a roof, use a 2x6 for the front rim, and a 2x4 for the rear. Cut a pair of 2x6's tapered from 5-1/4" in the front to 3-1/2" in the back to match the elevation change.
Use **** hinges to attach the rear of the roof to the rear wall, and cup-hooks or other latches to hold the roof frame down in the front.
Use standard galvanized (corrugated) roofing material for the roof.
Set the hutch on 12" square concrete blocks. If you set it on the ground, the 2x4's will rot out in short order.
Hope this helps.