One of the tools that I would insist is the most important tool in the shed when it comes to composting is the Garden or Composting fork.
There are several styles of forks and some are better suited for compost gardening than others.
The AMES 4 tine Forged spading fork
The AMES 4 tine Forged spading fork is the style of garden fork that I use most often. Its wide 4 wide tines and heavy construction make if great for digging over heavy materials in the compost pile.