Brooms

Material A
Metals.

Appropriate disposal: recycling.

All metals are recyclable for they change form to be easily melted.

Material B
Wood.

Appropriate disposal: Recycling.

It will be turned into wood mush! That will then be used for various other products such as biofuel and recycled wood flooring.

Material C
Plastics.

Appropriate disposal: Recycling

Plastics can be melted down as well, however not all recycling plants have the appropriate equipment, but chances are that they will pass that down to plants that can.

Best Alternative
Metals are the most durable and last the longest, therefore reduce the need to buy more again, however as long as you dispose of them well, the other two are okay as well.