How do I apply a custom set of blocks to a custom content type I have a custom content type I call a Listing. It contains a few hundred fields, and it has a custom template, which renders the node indie the main content area.

How do I configure the sidebar and other blocks to appear/not appear for only this content type and not all content?
This depends on the information you would like to show in the sidebar. If you want to show some static information like for example a help text, then you can create a block in admin / structure / blocks. After you added a new block, you can modify the visibility settings of this Block (and many other settings). For example set the block to to show only on a specific path, content type or whatever. 

The other way or case you might have, is to show dynamic data which has a relation to the content you're currently looking at. These dynamic blocks can be built for example with Views or you can create them programmatically in an own module. 

The placement of the blocks works like on the first case. But there are other ways to place a block (e.g with Context).