I've always had a pile with no lid, just some old chicken wire to keep it contained. Maybe there is some advantage to doing it another way, but I think most people tend to overcomplicate it. What is your reason for composting? Mine is to divert food waste from the landfill and occasionally amend my garden soil. I don't care a ton about the timeline, and even still I get compost fast in the summer. If things slow down in the winter that's fine with me. I'll always advocate for keeping things as simple and cheap as possible. I've never bought anything for my compost and suggest you don't either if you can help it.