Use plastic strips for the frame and rod for the bars.
Both Evergreen and Plastistruct make dozens of sizes of strips, often scale versions of common dimensional lumber (2" x 4", 1" x 6", etc)
mark the hole locations on one strip, stack that on top of several other strips and clamp if possible then drill the holes. Use one of these as a guide for drilling more strips. This will help ensure the holes are evenly spaced on each strip. Use liquid styrene glue, not superglue or the nasty gel plastic cement, it will have far less melting or mess. Cut the rods slightly then stack them so you can cut ends evenly and square. An adjustable carpenters square would work well, laying a ruler over the top should make a good cutting guide.