Currently, when I click on a layer, it automatically changes the channel to Quick Mask, which prevents me from working with the layer. Does anyone know which setting needs to be turned off in order to stop it from auto-selecting the channel?
You're in Quick Mask mode, which lets you quickly create selections/masks (seen as the red in the screenshot). Everything you do in Quick Mask mode is created on its own channel so that it can be turned in to a selection once you're done...
Turn it off with the Quick Mask button at the bottom of the toolbar (or hitting Q)