Rather than broom handles, if you are doing more than just enough for a meal, you can buy a folding clothes dryer (wood) which doesn't take up too much room and does a great job, especially if you are making the broader lasagna strips.
There are wooden pasta racks but they take up room on a counter or table, something that most people do not have.
Once the pasta is entirely dry, the best way to keep it is in a paper bag. The porous paper allows air circulation and keeps the past free of dust and critters that float around in the air.
One of my friends, who lives in a restored Victorian house in Pasadena got one of the clothes drying racks that hung from the ceiling in most Victorian kitchens. He uses it for drying pasta, noodles, etc.
